Single SNP testing of kit 462289, Iran funded by J2-M172 Hg Research has shown that J2a2-PF5050,PF5053(xL581,PF5058) indeed exists: tree.j2-m172.info/?Hg=J2a2
So L581 does not define all of J2a2 and can be again used reliably as primary SNP of J2a2a.
See also www.yfull.com/tree/J-PF5008/