Bummer i think it's built into the filter.
You could confirm the problem is in the pump or the FPR by pinch off the return line. There's a TSB on the exact procedure but if i did it i would have a helper so i can pinch the return line as soon as i turned off the key.
Or: i think foxwell can engage the pump. If your pump primes on key on you can listen for it to stop after ≈ 6 seconds.
The check valve is in the pump.
If pressure stays with the return line pinched the problem is like mine was: internal leak at the FPR draining. If it still drops it'll be the pump check valve.
If the pump check valve fails but the pump is ok, people will often just add an inline check valve.