hold hands with her and tell her I'm sorry for ur loss of ur father, husband
Ever since my father passed away my mom sleeps on the sofa is that normal cause she misses my father?
When it comes to mourning, it’s difficult to say what is normal. There is coping. This is how your mom is coping with the loss at this stage.
A friend of mine passed away a few years ago. His wife slept on the sofa for about a year and half afterwards. Many couples have their deepest connections while laying in bed. I am not talking just sex, but conversations as well. Plus listening to your other half snore or just rolling over and touching their shoulder. A bed can become very lonely after you have lost your spouse.
As for my friend's wife, when she was ready, she went out and bought a new bed, and redecorated the room. Sort of reclaiming the space as hers alone.
Your mom is missing more than the other parent of her child, or children if you have siblings. She has lost her life partner. And her sleeping companion. It will take time, but she will find her way, in her own time to move back to her bedroom.