How do you handle your Mom after Dad's passing?

Sorry to hear about your Mom's problems. If she had dementia/cognitive issues before her injury, TBI would certainly make it worse. In my opinion, make sure she can see any cards from their friends and pictures from his funeral. There is a lot for her to remember, and healing is a long time process. Just love her and tell her you miss him too.

What I have learned from my and other people's experience is that when she asks where he is, it is better to try to focus on her feelings in the moment than correcting her with the facts.
Since her brain cannot hold onto the truth of his passing, telling her repeatedly can cause her to relive the grief as if it is happening for the first time.

You can give a gentle, non-committal answer like "He isn't here right now, but I am", and then immediately talk about a happy memory of him or change the topic to something that will catch her attention

Saying "He isn't here now" or "I don't know where he is" is the perfect answer. With my cousin she would ask, and ask, and ask again. Made her upset and me frustrated/angry that she didn't seem to understand. I discovered making up a "story/lie" worked like a charm, she relaxed and I didn't have to answer again. Or sometimes, I just changed the subject, to lunch or weather or something that wouldn't cause her anxiety.
I had to remind myself of the serenity prayer, Accept the things you cannot change, and change the things you can"

I think my mother handled it fairly well but then she had dementia which, I think, in a sense, helped in that regard. My parents were married for a similar length of time. Eventually, my mother had to be placed in a home. Her needs became too much. It felt like a betrayal.

To your question, let your "patient" be your guide. Go along with it. If your mother asks something about him as if he is in the present, you can just say, "I don't know. We'll have to ask him." If she is actively seeing him (hallucination) you can ask how he looks or what he has to say.

It might be difficult but just remember that dementia is the most brutal thief of all. It is not your mom, just the thief that happens to be called dementia.

After my father-in-law died, my mother-in-law (age 80, but diagnosed with early onset dementia at 55) I began to spend more time with her and noticed what I called panic attacks, wondering where her husband/mother/grandmother were or what was happening. Prior to his death, my FIL would speak harshly to her and try to tell her that her grandmother/mother had been dead for 40 years and she needed to remember! The look on her face would tear your heart out, so I devised a plan . . we could be sitting quietly, me reading and her doing her beautiful needlework, when she would suddenly startle and ask, "Where's Ben???" (her husband who had died a year ago ) I learned the tactic of diversion . . . I would calmly tell her, "let me go see what he's up to," leave the room and come back shortly and announce, "oh, he's busy fooling around with that piece of woodwork (whatever) ," and she would nod her head and relax. She just needed to be reassured he was nearby and honestly, many times when I returned she would look at me and ask, "Are you okay? You left so suddenly." I realized then that these "panic attacks" were fleeting, as if a moment passed quickly in her thought process and was gone just as quickly. She also spoke of her grandmother and the good times they enjoyed together. Many times I would come to visit and she would tell me that she and her grandmother had spent the day together and had she had just gotten back into her room, at which time I would ask, "So what trouble did you two get into?" She would giggle and begin to tell me the adventure they had just shared. She seemed very content and I like to think she enjoyed reliving those wonderful times with her grandmother so who was I to tell her, "No! Your grandmother died years ago. Get it together!" The "diversionary tactic" worked until the day she died, and although I felt guilty at times lying to her, at least it calmed her, soothed her and allowed her to enjoy the peace and comfort her memories brought her. Hope this helps.

@vivi75 I think this is the sweetest and most humane thing you could do. You handled that beautifully. I shared on another thread where my husband did something similar with his father. FIL kept asking if his horse was outside. They lived in a suburb 5 miles from Stanford. My husband asked “what color is he, and I’ll go look?” FIL thought about it, then shook his head and started asking my husband how he was doing.

Diversionary tactics need some thought and/or training, but long gone is the option of reasoning, so to spare their feelings and your sanity, consider adding this tool to your toolbox. As my husband’s Alzheimer’s progresses - we’re in the early-mid stage, I’ve already started using minor ones.

Here’s to a hopeful new year.