I know it seems like an impossible thing to avoid, but I would really encourage your mom to hold out and not tell him that she’s passed away. That seems to open up another can of worms because then he becomes interested in getting his clothing out of the house.
Where does your dad think that his mother is? It sounds to me like, since he thinks he has clothing there, that he probably still lives with her or sees her pretty often. The first strategy I would try is to “get into his head” and really embrace his reality. Ask him about his mom. “When was the last time you got together?” “What do you do when you’re over there visiting her?” I once took care of a woman who believed that President Obama had been to her house. She told me this constantly, so I just started conversations with her about the President. She had really entertaining and interesting answers, and, the more she felt engaged in the conversation, the less she actually brought it up out of the blue.
Let him “call her” and leave a voice message. Have your mom call your cell phone, wait until it’s time to leave a message, and then hand him the phone. He’ll feel as though he’s accomplished his goal of reaching out to her, and you are validating his concerns.
What does your dad do during the day? If he’s engaged and involved in an activity (even if that activity is something like folding laundry) he won’t be asking about his mom. He’ll be focused on something else. Could he even put a gift together “for his mom”? He could help you make a scrapbook of photographs with the intent on bringing it to her.
The main thing is, and this is really the hard part, that your mom just has to accept the fact that he’s going to ask. She can make it fun for herself by coming up with interesting answers each time. “Oh, I just talked to your mom, she’s seeing some friends.” “We’ll see her really soon.” “Let’s wait until the holidays, I’m sure she’s really busy this time of year."
Hope these help!