Stalling

My car runs well for a 1994 Buick. At least it runs well with a full tank of gas. When the gas level goes under half full, it tends to stall. It starts and restarts very quickly. When I start out it runs well for the first 5 minutes and then stalls.It starts rigth up and does not tend to stall after it has run for 15 minutes. It never does this if the gas tank is more then half full. My local mechanic says it might be the fuel pump butit might not be since after 15 minutes it runs fune

Well, has your local mechanic actually used a fuel pressure gauge to find out what is going on with the fuel pressure?

How old is that fuel filter? Any check engine light?

He has not checked the pressure yet. I will have him do that. The fuel filter was changed within 4000 miles. There are no check engine lights.
Thanks for the reply.