Alternative solution:

Mike has a padlock which has a number combination. He sends the padlocked box to Jane and calls her to tell her the combination.

Alternative solution:

Mike has a padlock which has a number combination. He sends the padlocked box to Jane and calls her to tell her the combination.

Edit

If they have met before and he just wishes to send the ring via mail then they have already agreed identifying passwords in person, ensuring no Man in the middle can fake it.