I own an appliance repair service in inverness today after we had ordered a control board for a customer they refused to pay . is this theft of servi

This is simply a poor business model and you likely have no finaincially practical means of collecting. If this is a rare occurance its a cost of doing business. If its a common one you need to address this by changing policies such as having customer pay in advance for ordering parts or securing payments with credit cards, etc. You should also talk to a lawyer about having your paperwork changed from a simply invoice to some other structure or terms where you might collect legal fees for suing etc.