My step-father is very ill and 84. He has cancer and has been given 3 months to live. He has been married to my Mom for 57 years, they have been separated for 6 years and they don't speak to each other and he changed his Annuity out of her name as a Benificary and made his real daughter the sole heir to the annuity. It is about $ 120,000. She is on SSI and doesn't want to loose her status.
If she inherits the annuity and then signs the check over to my Mom will that work? She wants to give it back to my Mom and then she can live a little better than she has. What does that sound like. I hope I made this simple math for someone.

He made his bio daughter the beneficiary of his annuity. But she is willing to sign it over to your mom? The only problem here is this would be considered a gift to your mom and subject to gift tax. What she can do is gift $10K to your mom each year until the whole annuity is transferred.

I was writing about my sister taking the check and putting my Mom's name on it, does that mean my sister is out of the loop or what? She really is not the heir to this money, my Mom is. He is just angry that is why he took her name off, but really it is my Mom's money. I was thinking like a two party check, she signs the back and gives it to my Mom then my Mom is responsible for the taxes.

Doesn't work that way. You may consider it mom's money but legally, if the annuity is in his name, then its his to do with as he wishes. If your sister is named as beneficiary then its her money. If she wasn't to give it to your mom, thet's her prerogative, but it might be consider a gift and she may incur a tax liability for it. Your mom can give her back enough to cover the taxes, but she would have to pay it.