Lazhar, I would say the issue is 99% due to the fact that the archived folder you're using on your mac and mail client are local folders. As vukko mentioned (if I understand correctly), if this archived category isn't a subscribed folder via IMAP, you're not going to see these emails when you back to Gmail.
Instead of archiving, here's the workaround:
1) Create a new label in Gmail.
2) This label should show up as a folder on both your mac and phone clients (assuming you're using IMAP)
3) Instead of archiving, move your messages to this folder.
Cheers,
Ray