Existing Permit needs to be replaced. Once residence is estabilished it is not valid. Current wait times for LTCH seem to have returned to normal - about 2 to 3 weeks. It is best / fastest to use the electronic filing and electronic fingerprinting. The lifetime LTCH is best.
Also - in Indiana - it is a License to Carry a Handgun (LTCH) - the method of carry, and what you carry, are up to you.