I am asking this question for a friend

I just turned 18 and mom used my name to open a credit card.

She spent 500.00 on card, then somehow my evil brother got a hold of it and in 1 week withdrew 2000.00. Somehow he knew the pin number. He is a pro at scamming people out of money. I think he knew my SS number and got it that way. My mom was really mad when she found out he did that even tho she started this whole problem. She tried to get pictures of him taking it out of the ATM but they had no cameras at that location.

No police report was filed and really doesnt want to file one on his mom for this.

He is an honest college student with a bright future and now his credit is really messed up.

Credit agencies wont even help because the fraud came from the same address. He lives with his mom and brother.

How does he fix this problem without getting his mom arrested? He doesnt want police or court involved

If you want to "fix" this without filing a police report,you will have to be responsible for the the bill.
You can take your mother and/or your brother to small claims court and get a judgment against them. It will be a civil judgment so there will be no criminal record.
In the future you can put a fraud alert with the credit bureaus so you can be notified if anyone tries to apply for credit using your information.

Three options:

Pay the debt himself (contact credit company tell them what happened, tell them he can't press charges against his mom and then ask for them to halt interest and let him make payments to pay it off. Try to get money out of brother and mother to pay. Doubt he will though.

File police reports against both mother & brother. Follow through and help the prosecutor file charges. Possibly get out of paying debt, mother & brother would be ordered to pay you restitution that you can use to pay off card.

Do nothing and ruin credit for a long damn time. Eventually be sued and owe much more than he does now. Have to pay it off before he could ever buy a home.

It sucks when family screws you over. You end up screwed twice.