First, lets clear up some misconceptions:
In the early war Germany was at the forefront in the development and use of tanks
No. It wasn't. German tanks were not superior to allied tanks. Allied tanks, one tank against one tank in a battle of mobility, armor and firepower, outclassed the German tanks of the time. The guns mounted on the German tanks, even the "modern" Pz. III that was supposed to go against other tanks with it's measly 3.7cm gun was unable to penetrate the British and French models like the British Mathilda or the French S35 and B1 except for maybe lucky hits on specific weak spots in the side or rear armor. And that is assuming the Germans even had a Pz. III, the bulk was made up of Pz. II, which did not even have something meant to destroy another armored vehicle.
So how did they win such astonishing victories then, if the tanks were so underwhelming?
Well, warfare isn't a tank on tank fair duel of mobility, armor and firepower. Tactics make a huge difference. It's called "combined arms" for a reason. And even just between the tanks, there was a huge difference in potential. Because the communication and using communication between tanks to act as a team and support each other instead of just every tank fighting on it's own or by a predefined plan is super important. Even more important than having more mobility, armor or firepower. Just imagine a computer game today, with one team using a voice-software to communicate and react to the gameplay as it unfolds and the other team just having had a talk before and then everyone just giving their best with no clue what their teammates are doing or how the team is doing in general during the game. You can easily see how the team communicating in near real time will wipe the floor with the team not communicating at all, regardless of how good the individual players are.
The German tanks had short distance radios by design, so the tanks could communicate with each other or at least with their leader. And the leader had a longer range radio, so they could communicate with their superiors and transmit information and get new or updated orders. All under the cover of their armored vehicles, all in real time. The German design of most tanks had an extra crew member (compared to competing designs from other countries) to be able to communicate and keep fighting at the same time. So this was not just a box of additional technical equipment, this was a conscious decision to improve tanks and their function on the battlefield in this direction. The French, and I kid you not, had to open the hatches of their tanks, stick their body out and wave flags and then hope the other tanks accidentally saw them through their tiny view ports and could decipher what the flag waving meant. Some had carrier pigeons to carry their updates of their attack to their superior officers in the back. I don't think I need to tell you how hopelessly inefficient that was and how the German tacticians ran circles around their counterparts. Reacting to an unfolding situation on the ground and mounting an attack took the Germans a few hours in the battle of France. Mounting a counter attack took the French days. Plural. Days.
Then later on the Eastern Front, again, the German tanks were outclassed. A T-34 is a brutal machine, there is no way a Pz. III or even an upgraded Pz. IV would have a chance in a one-on-one duel between equal commanders. But it's war, not a pirate movie. There are no duels. There are no equals. Nobody ever went to war aiming for an equal, fair fight. While Russian T-34s again were superior in mobility, armor and firepower, their tank crews were inexperienced and badly led, by their even more inexperienced commanders. It was a slaughter. The combined arms warfare with the added much greater experience of the operators proved to be superior to just having the statistically better machine.
Only when the Tiger and Panther appeared, you could say that the German tanks on a tank-by-tank basis, were the better machines. But by then, the other factors of the war had shifted against them. The weaknesses that were once deemed acceptable when they were designed years earlier with the German army fighting fast advancing maneuver warfare battles, were now deadly. For example, maintenance problems are minor problems when your side advances. You pick up any tank that was left behind on the attack, repair the minor problem and send it back into battle. But if you are defending or retreating, any tank with small maintenance problems becomes a casualty immediately. It will end up in enemy hands, or you can destroy it yourself when you retreat and cannot take it with you because something broke or you ran out of fuel or other consumables.
So, to sum that up: German tanks were never "better" than their counterparts. At least not when Germany was winning their impressive tank warfare victories. They were better coordinated, better lead and better crewed than the average enemy though and that is what had them win.
So back to the original question, keeping in mind that captured equipment was mostly on-par with German equipment from the point of pure performance statistics. Not equipment Germany could produce in the future, but compared to equipment Germany had on the battlefields right then:
There were basically three ways the Germans used "foreign" tanks:
They got hold of the factories, deemed the tanks "good enough" and continued producing them.
This happend with the Czech tanks, named Pz. 35(t) and Pz. 38(t), where (t) stands for "tschechisch", German for "Czech". Those tanks were solid designs and better than what the Germans had as their bulk force, the Pz. II. Even when the German tanks improved and the Czech designs were considered just as obsolete as their German counterparts of the time, they kept the factories to produce vehicles based on those chassis. Even if outdated for main battle tanks, you can still use them for self-propelled artillery or tank destroyers, that don't need that kind of armor protection. It does make sense to produce two or three outdated tanks or mechanized vehicles instead of a single one brand new, slightly faulty, expensive vehicle. War is no beauty contest. "Good enough" can kill the enemy, too. And especially in areas where you don't encounter enemy frontline combat troops, where the enemy is not as well equipped or maybe even militia or partisans, a tank 3 years outdated is still an unbeatable monstrosity. And in garrison functions, the need for replacement parts is not as bad as in high attrition areas, whether it's combat or just the environment in general.
They captured equipment. Tons of equipment. That happened with the French armories and early Russian positions that were overrun. And they needed vehicles they could not produce themselves on short notice. The war against the French and then early encounters with T-34s and KV-1s had shown their tanks lacked serious firepower. And firepower is not a problem in general, bigger guns always exist. The problem is that the tank design cannot house a bigger gun. Not without a bigger turret. And the bigger turret would need a bigger chassis. So a bigger gun would need a complete new tank design. That can take years. However, if you take a current (or even outdated/foreign) chassis and strap a gun onto it, without a turret (accepting the fact that this is not a full tank, just a mechanized gun carrier with some light protection for the crew), then you can have a bigger gun that is mobile and can penetrate enemy armor your actual tanks cannot. And since this is not exactly a design choice, but a kind of stopgap measure until your new tank design is actually done, you can take any gun and any chassis. If they already exist and don't need to be built, all the better. That is how the Marder line (and a few other weird patched together vehicles) came into being.
And third, just plain reuse. If you capture a T-34, after you sent the first few to "Erprobung" (intel gathering) to Germany, why would you not use them. This was not any type of plan or strategy. But war is rarely about well executed strategy. It is makeshift and improvised and as such they used every tool they had. Even if it breaks down due to maintenance problems because you have no spare parts or the wrong kind of fuel or no ammunition... using it until it breaks is still better than breaking it on purpose, or leaving it to the enemy.
Was the use of captured tanks an effective strategy for Germany?
Yes. I mean what was the alternative? Just not do it, dump the weapons somewhere and go in for a boxing match bare handed? Even with factories captured, you cannot just retool them at a moments notice to produce another type of tank. Retooling a factory costs time and money, while it sits there and produces nothing for while. And the Germans had proven that their victories were not due to better tanks, but due to better tactics. So factories produced obsolete tank models (or at least their chassis) to be used in other vehicles, that were still useful.
I'm not sure if "effective strategy" would be a good description though. They did not plan to do it. It wasn't part of some global strategy. It was more like "if this is the best option we have, why not use it". And yes, it was the best option and they did use it.
