19th century Box with Miniature Portrait

A beautiful 19th century brass pill or snuff box, decorated with a very pretty miniature portrait on porcelain. The portrait is signed ‘Brodel’ who I believe to be Ernst Brodel, and is stamped on the back as the Duchess of Exeter after Thomas Gainsborough. However, I think this is incorrect as there was no Duchess of Exeter in Gainsborough’s time. A closer match would be Georgiana, Duchess of Devonshire. The portrait is of her likeness. The box measures 9.5cm in length and 8cm across.