Catalysis of the reaction: 1-alkyl-2-lyso-sn-glycero-3-phosphoethanolamine + 1-alkyl-2-arachidonyl-sn-glycero-3-phosphocholine = 1-alkyl-2-lyso-sn-glycero-3-phosphocholine + 1-alkyl-2-arachidonyl-sn-glycero-3-phosphoethanolamine.
1-organyl-2-arachidonyl-sn-glycero-3-phosphocholine:1-organyl-2-lyso-sn-glycero-3-phosphoethanolamine arachidonoyltransferase (CoA-independent)