The Painting is a Major Item in The Twins. It is part of the three most valuable Items in the game along with the Gold Coin and the Diamond. It can always be found in the exact same place, being the Metal Case stuck to the Main Room's left wall, near the ceiling. This Item, being a Major one, is evidently always required to escape as it is needed to complete your Mission in the Abandoned Prison, and that, even if completely unlocked and the other two Major Items in hand, none of the three Escape
The Twins Official Wiki
Abandoned Prison, The Twins Official Wiki
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File:Chang and Eng, Siamese twins, 1836. Oil painting by Edouard
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Han Solo: In Carbonite Removable Wall Decal
File:John Everett Millais (1829-1896) - The Twins, Kate and Grace