Catalyzes the transfer of adenosine 5'-monophosphate (AMP) to Ser, Thr or Tyr residues of target proteins (AMPylation). ATP + L-tyrosyl-[protein] = diphosphate + O-(5'-adenylyl)-L-tyrosyl-[protein] ATP + L-threonyl-[protein] = 3-O-(5'-adenylyl)-L-threonyl-[protein] + diphosphate ATP + L-seryl-[protein] = 3-O-(5'-adenylyl)-L-seryl-[protein] + diphosphate Belongs to the SELO family.