Is it possible to transfer from one independent living community to another without having to pay a second entry fee?

Sorry, but the same happened to my mom when her sister passed in a 2 BR apartment and she had to pay a new enrolment fee in the same IL to go to a 1 BR. Each vacated place requires some updating such as new carpets. Read the contract. Sometimes you can get a partial rebate if the apartment is in good shape.

I had an ALF offer to wave the community fee in order to get DH aunt to remain. She had been there for a short time.
It’s all about what the market will bear in my very limited experience with ALF.

Could always ask for it to waved, anything is possible and worse they can say is no.

Not if they are separate run Communities. If they are run by the same company, maybe. That is a question for the Community ur in now.