Catalyzes N-methylation of phosphoethanolamine, phosphomonomethylethanolamine and phosphodimethylethanolamine, the three methylation steps required to convert phosphoethanolamine to phosphocholine. phosphoethanolamine + S-adenosyl-L-methionine = H(+) + N-methylethanolamine phosphate + S-adenosyl-L-homocysteine Phospholipid metabolism; phosphatidylcholine biosynthesis; phosphocholine from phosphoethanolamine: step 1/1. Belongs to the class I-like SAM-binding methyltransferase superfamily. PEAMT family.