From AMLopedia
The vest is a green vest originally owned by Liam's mom, Cathy Green. She made it out of a vest kit sometime in the 80s. All the sewing was done by her. Liam used to wear this vest a lot to Boy Scout campouts because it was so warm. When he wore it to a LAN Party, Adam got jealous and decided to steal the vest, just like he has done many times with the hat. He owned it for a while before Liam stole it back. The vest currently resides at Liam's house (I think?)