Local historian Denis Rose donated the photograph to the borough after Wirral Council purchased the original wooden cross placed on Frank's grave in Neuvilly, Le Cateau, where he fell.
The council did not have enough money to buy the VC which was auctioned for £78,000 at the same sale. Mr Rose, 77, who handed over the picture to Mayor Patricia Williams, said: " People don't realise that the VC is the highest honour that a country can bestow.
"King George said it all in his letter to the Lesters when he described it as the 'greatest of all rewards fo r valour and devotion to duty'."
Corporal Frank Lester was born in Huyton and his family moved to Hoylake, Wirral, when he was a baby in the late 1890s.
He enlisted in the Army and was drafted to France in December, 1917, as a member of the 10th Battalion of the Lancashire Fusiliers.
On October 12, 1918, he was part of a team clearing the village of Neuvilly after the Allies finally overhauled the Hindenburg Line.
Frank entered a house and shot two German soldiers, but falling masonry blocked the group's exit. The only way out was being peppered by an enemy sniper.
Dashing out into the street, Frank, 22, shot the sniper but was killed by return fire.
His citation for the VC said: "To save their lives, he sacrificed his own."
The remaining members of the Lester family decided to put the medal and cross up for sale in April.
Frank Lester's nephew Frank Wilson, 68, said: "The family were all very proud of him but it had got to the stage where the medal had become a liability.
"When you talk of the value involved, we couldn't afford to insure it and if you put it in a bank vault you don't see it so what's the point in keeping it.
"Reluctantly, we decided to sell it."
Wirral Council bought the cross for £1,000 at London auction house Morton and Eden.
Both the picture and cross will go on display in the heroes' gallery of the museum in Birkenhead Town Hall this autumn.
Acting principal museums officer Colin Simpson said: "The museum has only been open a year and is now increasingly the focus of our local history collections.
"The cross is sort of a personal contact with Frank Lester himself.
"We are aware of the interest in a variety of service people like Frank Lester.
"I think collections like this are and should be part of the local community because we reflect the history of the society we live in."