I purchased Infuse Pro Lifetime License back in June last year but never able to get it working with Apple Family sharing.
License works fine for me as purchaser, but it doesn’t work with any family members - even though all members in my Apple Family Sharing has both Subscription and Purchase sharing turned all bi-directionally. I also tried flesh install of the Infuse App on iPhone, iMac, iPad, Apple TV using a family members Apple ID but nothing works (i.e when clicking on the “Restore” button in Infuse License dialog, it spins for a second but does nothing).
You may want to read through the users guide for family sharing. That will give you some trouble shooting help and also some options to try including using Trakt. You can find that guide here.