If a Barbarian/Sorcerer multiclass casts False Life on himself, then rages, will the spell's effect remain active?

Question

In an adventure I am playing, I play a barbarian 1 / sorcerer 1, and I am in a dispute with my DM. My DM says that if I cast False Life on myself, then Rage, the spell's effect will not remain.

Page 48 of the Player's Handbook says, under the description of the Rage feature:

If you are able to cast spells, you can't cast them or concentrate on them while raging.

Because of this rule, am I able to keep the effects I cast on myself?

Answer 1

Yes, because False Life does not require concentration.

The false life spell has a duration of 1 hour, and doesn't require concentration.

Because it requires no concentration, if you cast it before raging and your rage occurs within its one-hour duration, the spell will still be in effect.