Sir Rupert Archer is the thief!
He does not have a twin brother. The portrait of 'Henry' is his own self-portrait.
To paint a self-portrait one must look into a mirror. A mirror, as we know, reverses our image. If one does not have a symmetrical face, and most people don't, then a person's mirror image will not look like the person. They may look similar but they will look like two people, and could be mistaken for identical twins but with tiny variations.
Sir Rupert was aware of this asymmetry. Suddenly he saw how he could use asymmetry to steal a Rembrandt. He painted his self-portrait but said it was a portrait of his twin brother. He hung it in the Gallery for all to see. When the exhibition was under way he made a copy of his favourite Rembrandt. After closing time he removed this particular painting and hid it among paintings awaiting repair in the Gallery's workshop. He then set in train his reporting of the theft. His intention was to collect the painting after enquiries had quietened down or been abandoned. If things had gone wrong it could 'accidentally' be found in the workshop. Either way, he was safe.
Having secreted the Rembrandt, he now needed witnesses to see his 'brother' ostensibly making his escape with the painting. Late at night he took his replica of the Rembrandt and hired a hansom cab to take him to the waterfront of London's East End. This was to cause the police to think he was escaping to the Continent by ship. He made sure that one or two still about the streets at that late hour saw his face and saw his 'Rembrandt'. Under the gas-lit street lamps his facial features could not be distinguished with any precision. Once on the waterfront he defaced the painting and threw it into the Thames and then returned to the Gallery. He made his late inspection of the Gallery and then, after waiting for a policeman to come into the street on his beat, raised the alarm that a Rembrandt had been stolen and his brother missing.
When the police brought the witnesses to the Gallery Sir Rupert ensured he was out of their sight and the police had no reason to bring him to their notice. Each witness, in turn, when shown the portrait of 'Henry' immediately declared, "That is the man!" How safe Sir Rupert must have felt with the police searching for his non-existent brother.
Then Sherlock Holmes came to the scene! The 'equipment' Holmes brought to the Gallery and handed to Watson was nothing more than a tiny mirror. Holmes had his back to the paintings to enable him to see Rembrandt's reflection in the mirror and what he really looked like. Watson was still using the mirror when Sir Rupert hung his painting. When he saw Sir Rupert reversed and the painting reversed he knew who was guilty and that Sherlock Holmes had solved yet another crime!