*** Moved from K1 Process & Procedures to AOS from Work/Student/Tourist Visas forum -- OP's fiance is already in the US, considering staying after marriage ***
Then marry him today and file the I-130, I-485, I-131, I-765 as soon as you have a valid marriage certificate. As others mentioned, there's no need to wait 90 days. The sooner you two file that I-485 package, the better his chances of getting that AP sooner to travel outside the US without jeopardizing his GC application. After his biometrics appointment, he may also request an expedite for his I-131 AP processing to visit his sick parent. No guarantee it will be approved, but it wouldn't hurt his case to request one.