Dressed in a suit, he handed out currencies in exchange for sterling to customers at the Asda in Trafford Park, police said.
He then emptied the safe into a bag before walking out of the store at 15:45 BST on 29 July.
Police said they were still searching for the man, described as in his mid 20s or 30s, Asian and of slim build.
A 22-year-old woman has been arrested and bailed on suspicion of conspiracy to defraud.

The West Indian Carnival in Leeds was launched in 1967 and once again will take over Potternewton Park for the August bank holiday weekend.
An exhibition recording its heritage, political and cultural legacy is planned for the city's Tetley gallery.
There will also be a week of new plays commemorating carnival at West Yorkshire Playhouse.
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Additionally, it has been announced that an illuminated night carnival will kick-off the annual arts and light festival Light Night in October.
A recreation of the Sun Goddess, the first Leeds Carnival Queen costume, will be featured at the exhibition from August to October.
The celebration of food, music and culture will culminate again in a parade through Chapeltown and Harehills.
An estimated 160,000 revellers attended last year's carnival, organisers said.
Arthur France initiated it after becoming homesick for his native St Kitts and Nevis.
Mr France, head of the organising committee, said: "When you come to carnival it is electric, so many things going on, beautiful costumes, beautiful colours, beautiful music."
However, attempts to bring the parade into the city centre have been shelved.
Mr France said he was "very sad and upset" at the council decision but added that it would not "dampen my spirits".
Councillor Judith Blake, leader of Leeds City Council, said: "A lot of events are happening on the bank holiday weekend and with the advice it just wouldn't be possible."
Ms Blake added: "The oldest carnival in Europe is here in Leeds. We are so keen to make sure as a city we come together and everyone celebrates an incredible achievement."
She praised Mr France as a "legend" that had made "an absolutely fantastic contribution heading up a brilliant team of people".

Of the 863 men who died, an estimated 120, known as "the Jersey Pals", were killed during the Battle of the Somme.
Made from Jersey granite, the memorial stone was officially unveiled by Bailiff William Bailhache in the French village of Guillemont.
The delegation from the island also included the Lieutenant Governor, Chief Minister and the Dean of Jersey.
Ian Ronanye, an author and historian, said the memorial would be a permanent reminder of the role Jersey played in the great war, although part of it would return to the island.
"A core has been removed from the middle of the stone - about the height of a person's heart - and that is being brought back to Jersey to become part of a monument in Royal Square," he told BBC News.
In July, hundreds of people attended a ceremony to reveal the memorial stone.
A man has walked away with £40,000 from a superstore in Manchester after posing as a manager at the Bureau de Change.
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Plans have been announced for the "oldest carnival in Europe" to celebrate its 50th anniversary.
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A memorial dedicated to the Jersey men who died in World War I has been unveiled in the Somme region of France.