"They have asked Facebook to remove the posts but that hasn't happened," Heath said on Friday.
"I can't see why they can't get him in a room and get him to remove the posts or disable his account," she said.
"It's like he's on holiday with getting new tattoos and messaging his mates."
Thompson pleaded guilty in September to stealing $16,000 worth of pounamu, or greenstone, from Heath's Waikanae gallery in February.
He received a one year and three week sentence at Rimutaka Prison for the burglary, and for driving and drug offences.
Heath was alerted to the posts on Corey Thompson's Facebook page. She was then contacted by Corrections after they too had been made aware of the posts.
He was still posting from prison on Thursday.
On Boxing Day he told posted about his Christmas Day meal.
"Yea my bro roast chicken and apple pie n custard but made cakes n s*** wif farmbakes ect was pretty good ae i was stuffed yesterday and today had leftovers mean as haha lol."
Heath said she was outraged for all victims.
"I can't see how, if they are not allowed phones or computers in prison, he is able to be on Facebook."
"It's like he is on a tax-payer funded holiday."
Prison contraband includes cellphones, weapons, drugs, food, tobacco products and pornography.