If you own a iPhone, you can configure the built-in email client to read your Gmail, and later bring up Gmail in the browser for archiving inboxes. The default Gmail set up for iPhone’s client trash a message in 30 days, when you click delete. But if you want mail you delete on your iPhone to get archived, you just have to re-do the Gmail set up on your phone.
First, go to Settings > Mail, Contacts, Calendar. Find your Gmail account under "Accounts," click on it, scroll to the bottom, and click "Delete Account." Don't worry -- it'll be back and better than ever in a sec. Then manually configure IMAP using the "Other" menu option by following the instructions the video below.
From then on, the iPhone's little trashcan icon will archive your mail. You might notice that messages you archive on your phone are actually being added to a new "Deleted Messages" label in your Gmail account -- but they're right in "All Mail" and searchable, just the way you want them.
Tip: To find when you created a Gmail account, go to "All mail", click on "Oldest" and you'll see the first messages you've received. You'll need this information to get access to a compromised Gmail account.
Source:→ Gmail Blog