Baxter joined Everton at the age of six and progressed through the youth ranks before becoming the youngest player to debut for the club at the start of the 2008-09 season at the age of 16 years and 191 days.
The 21-year-old joined Tranmere on loan in September 2011 after only making a handful of first-team appearances for Everton and enjoyed the experience of playing regularly so much he had no qualms in turning down a new deal with the Toffees when it was offered later that season.
Instead, Baxter signed up for npower League One side Oldham where he has been an ever-present this season, scoring 11 goals, and playing his part in dumping Liverpool out of the FA Cup fourth round three weeks ago.
Now Baxter takes on his old club in Saturday evening's fifth-round clash at Boundary Park, with Moyes believing he made the right decision last summer, and it will reap further reward.
"I'm delighted for Jose," Moyes said.
"We gave him his debut when he was 16 years old, and it's hard when you come in that early because by the time you get to 19, 20, people are beginning to ask 'Where are you? What are you doing?'
"He probably found it a struggle getting into the first team very early, so we put him out on loan.
"We then offered him a contract and he could have stayed, but the boy wanted to play, so he chose to go.
"I admire that because there are a lot of players who don't choose to do that, who would prefer to sit and hang around.
"It was a brave decision for Jose, and hopefully he sees it as being the right one for him."