Well it happened to my niece and myself. Started with my niece posting dresses on "let go". when the check arrived it was 1500 over. she said her name was Christina Scott husband had messed up and sent the entire amount of money to me instead of dividing it up between me and the movers. said the person who would be picking up was someone by the name asked to please help her make sure the money goes to the right place. never once thought it was a scam until the next day. check hasn't bounced yet but I'm sure it will. I have the mailing envelope, wire transfer and name to person money was going to. at the time I didn't think anything about it. I thought I was helping out a lady with 3 kids and a stupid husband. well, who's stupid now. going to make a police report this afternoon. Cristina Scott was texting/hounding me all day on Friday. by the end of the day, it never registered I was sending to a Cristina Torres in GA. Just realized yesterday it was the same name.
Yes the check is fake-I would contact your bank and fill them in. Also the post office may want to see what you have left as it could constitute mail fraud. Here is a link to the FTC and an article about fake checks. https://www.ftc.gov/search/site/fake%20check
Learn and move forward. Good luck.