Adenylyltransferase that mediates the addition of adenosine 5'-monophosphate (AMP) to specific residues of target proteins. ATP + L-tyrosyl-[protein] = diphosphate + O-(5'-adenylyl)-L-tyrosyl-[protein] ATP + L-threonyl-[protein] = 3-O-(5'-adenylyl)-L-threonyl-[protein] + diphosphate Adenylyltransferase activity is inhibited by the inhibitory helix present at the N-terminus: Glu-224 binds ATP and competes with ATP-binding at Arg-364, thereby preventing adenylyltransferase activity. Activation dissociates ATP-binding from Glu-224, allowing ordered binding of the entire ATP moiety with the alpha-phosphate in an orientation that is productive for accepting an incoming target hydroxyl side chain (By similarity). The fido domain mediates the adenylyltransferase activity. Belongs to the fic family.