On March 9 it is believed that the home on Fitzwilliam Road was targeted and the two boxes, one belonging to PAWS and one to Yorkshire Air Ambulance, were taken.
Joe Talbot, of Briery Walk, Greasbrough, was arrested on March 23 following police enquiries.
The 51-year-old was remanded in police custody.
He will appear before Sheffield Crown Court on April 21.