The former Ibrox director states in a CV for his new financial advisory company that he oversaw the flotation of the club plc on the stock market, which generated funds of £22 million "and secured Rangers' future".
Union of Fans spokesman Chris Graham described Mr Stockbridge's claims as ridiculous.
He said: "To suggest that he has somehow aided Rangers is fairly ridiculous given everything that has happened since the takeover.
"He is happy to take credit for the fact the money was raised, but doesn't want to take responsibility for the contracts that were in place that took the money back out, no responsibility for where the company is now with all that money gone."
Mr Stockbridge was an associate of former chief executive Charles Green, who, with partner Imran Ahmad, put together the £5.5m deal to buy the liquidation-bound club company business and assets in June 2012.
Mr Stockbridge, who received a £200,000 bonus for the team's success, left the club in January.
He has now founded London-based International Financial Strategic Associates, through which his claims about his Rangers achievements are made.
His CV states: "He was also instrumental in rescuing Rangers Football Club from certain collapse at a time of unprecedented crisis.
"Working as finance director of the club - under intense media scrutiny and without the support of a full board for months - Brian restructured the club's finances, oversaw the flotation on AIM, which generated funds of £22m and secured Rangers' future."
A spokesman for Mr Stockbridge said he stood by his claims, adding: "While the debate around Rangers will always be a heated one, without the actions taken at the time there is a very real possibility that there would be no club now to discuss."