FIRST OF ALL, don't hijack other's thread. Just create a new forum topic, clearly explain your issue and paste related log to help troubleshoot.
Looks like it doesn't perform SMTP AUTH at all. Is it possible to enable debug in Postfix for (just) this client? You can achieve it with below steps:
*) Set below settings in Postfix main.cf:
debug_peer_level = 2
debug_peer_list = xx.xx.xx.xx # <- This is IP address of the end user which has issue*) Reload postfix service, then check its log file.
*) Try to reproduce this issue by sending a testing mail from this end user to you(?), paste full smtp session log in Postfix log related to this testing email here.