Complex sentence: He specified in his will that should his bequest be refused by Hampstead (presumably on grounds of propriety) the painting was then to be offered to Coventry.The painting now hangs in the Herbert Art Gallery and Museum.
Split into simpler sentences: He specified in his will that should his bequest be refused by Hampstead (presumably on grounds of propriety) the painting was then to be offered to Coventry. That was what happened, and the painting now hangs in the Herbert Art Gallery and Museum.