The fuel pump does indeed have a check valve.
I should have spent more time with my previous answer. My mistake! The filter is primarily the fuel pressure maximum regulator, filter, and with a return line to the fuel tank to bleed off excess pressure.
The pump is designed to hold fuel in the line at about 36 lbs. pressure after the car is shut down. So it would be normal for the pressure to decrease at the fuel test port to 36lbs after shut down. The pump's check valve should hold that pressure in the line until the ignition switch is turned on and thus the pump should bring the pressure back up to 55~60 PSI at the test port. With fuel being held in the line the pressure will rise very quickly and allow ignition without hesitation.
There is also a possibility that a fuel injector is leaking and allowing the fuel pressure to drop. You could distinguish between the two problems by were you place the pressure testing gauge.
Sorry about my post #14 above being incorrect/incomplete.

 

My slow/hesitant to start when warm issue has been resolved. Many thanks to all members for their wise advice and sharing past experiences.
I did order a XF fuel filter and fuel pump from RockAuto. This past Tuesday, I did swap out the old filter and pump.

After reading the service manual chapter 14, fuel system, at least 3 times, I realized that there is a check valve in the fuel filter and a check valve in the fuel pump.
Chapter 14-4 did say a quick loss, as in my case, was probably due to a defective pressure regulator in the fuel filter. I took no chances and replaced both filter and pump. Now when I turn off the engine, the pressure stays in the engine fuel rail.

Rupert

PS amazon.ca sells the XF fuel pump for $45. to $335. crazy. I guess there is one born every minute.

 

I thought I would post what I found on part numbers for the fuel pump. Please correct me if these numbers are incorrect.
Crossfire: 05102594AA, N/A and SRT are the same.
MB: 000-470-78-94-80
Bosch: 66150

 

Never use the Chrysler part number unless you want to pay top dollar for the item, use the Mercedes part number.
Better yet use the Bosch or another good brands number.

 

Normally I know enough about car repair to just be dangerous (unless for MG Midgets). However, after reading this thread I was able to have an intelligent conversation with the repair shop that replaced a failed Bosch fuel pump and filter in my 2006 XF roadster 7 months ago. Recently my '06 started cranking for a long time before start, and sometimes it took a second cranking. It would run rough for a couple seconds then smooth out. Told the repair shop it sounded like the fuel rail was losing pressure after the engine shut off and the check valve in the new (7 month old) pump might be the culprit. They tested the pressure and found that after engine shut down the pressure went from 60 to 15 immediately. They confirmed the fuel pump was bad. The replacement pump they had put in was a Delphi FE0346 which is supposed to be even better than the original Bosch 66150. They are replacing it now under warranty. Felt good to know what I was talking about with them and they seemed impressed that I did. When I was telling them what I thought the problem was they were all nodding their head in agreement. First time that's happened. Anyway, thank you for the info and for allowing me to be more knowledgeable than just dangerous. Score one (of many) for the Forum.

 

I’m glad that the information I learned was able to help someone else. It took me a while to figure out it was the check valve in the fuel pump and I wasn’t able to find much information on it in the forum. There have been other issues which I found solutions to hear and saved a lot of time and probably a lot of money on by searching the forum first.