How do I fake a phone call with a dead person?

I wouldn’t fake it, it will only make the delusion persist. Very understandable that the excuses you’re using are exhausting to you, but coming up with a fake dad will likely be even harder on you. Hope she’s receiving a med to calm her anxiety

Even if you do have someone play the part of a dead person, there's a good probability that Mom won't remember that conversation.

You'll be back where you started.

This will pass.

Even long term loops always do.

My answer depends upon if you are living with mom. You can disconnect the landline at the wall so she will only discover that the phone line is out. You can then use the excuse of it will take x time for the repair or that you need to go home in order to call the phone company.

Can someone play Dad. They don't have to carry on a conversation, just give her the OK.

I would think your Mom has been told, at one time, that Dad is gone, she just does not remember. And if you tell her now, she won't remember tomorrow. Some go thru the whole griefing process again. You can tell her again, but don't be surprised when she wants to talk with him tomorrow.

You don't. This is the sort of desperate action that dishonesty leads to in these cases. She should have been informed of the truth. And should be informed now that he is gone.
How does one thing that a right to know and to have grief is taken when everything else has already be stripped away?
Just my humble opinion. You must do as you think best for the person you love.