84-year-old father thinks my mother is secretly living in home. She has been deceased since June 2023. He says nasty things about her.

Depending on what he says, and you didn't give an example, could you play along with it? Such as, "I'm sure we'll find her soon?" If you'd agree with him instead of being oppositional, that might defuse his anger.

I'm very sorry, it must be so painful for you.

I played along with my mom's delusional ideas, and it seemed to work. She was sure there was a dragon or dinosaur on her screened porch. She was afraid of it. I let her talk about it and would say something like, "At least it's gone now." That shortened the conversation so we could move on to the next topic, sometimes also delusional.

I guess he must miss her plus also be angry with her for not being there.

He can't see her - he 'reasons' she must be hiding.

Do photos of your Mother help or make it worse?

What about older photos? Dated from when they were newlywed? Often the long term memory is much better, so reflecting back on the distant past can trigger happier feelings.

I’m so sorry. I’m sure this is very hard for you to see.

This happens with dementia, and it is, yes, so very sad. I am so sorry.

How very sad that he doesn't remember that she died just a few months ago. Did he go to her funeral, and was there an obituary that you could show him when he gets mad or nasty towards her? Or if she's buried somewhere you can take him to the cemetery to visit her gravesite.
I understand that logic doesn't live here anymore when dealing with someone with dementia, so you're just going to have to keep on trying things, even therapeutic lies if necessary to try and keep him calm.
Best wishes.