Anyone know how to KEEP all your emails from Gmail??

[efunk33]

I can download my emails just fine, and all my folders I have setup in gmail are there, but I can't get any emails to stay on my phone in those folders. I understand I probably can't get the emails from before I had my phone, but I would think all the emails I get now on my phone, I should be able to move them into a folder on my phone, and have them stay in that folder(like archive them), and they would move to that folder in my gmail account when I checked online too.

Only place emails stay are my inbox. If I have 5 emails in my inbox online, they are all there on my phone. If I move one of them to a folder from my phone, it leaves my inbox on my phone like it should, leaves my inbox online like it should, goes into the folder online like it should, but does NOT go to that folder on my phone.

Basically, my phone only stores emails that are in my inbox. I want to be able to store all the emails on my phone, that I have online.

Make sense?