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Sounds like you need to set it up as a "Pop" email account, not an "IMAP" account... Pop downloads to your phone, but doesn't delete from the server... This works if you are using a 3rd party email app such as "Mail" or "Outlook", but doesn't work if you are accessing the gmail via web-based application.
 
Again Thanks.

+1 "Thank you danielj. You answered the question and solved the problem instead of editorializing or asking WHY the user wants to delete from her iPhone and not her computer."

99% of email done on computer using Thunderbird and gmail accounts. When traveling, in town, will use one of many iOS devices to check mail for many email accounts. Don't want bits and pieces of emails left of various machines but want all to eventually end up on computer.

Several years ago on iPhone 4, an earlier iPod Touch and original iPad found instructions that worked. In various device/iOS upgrades lost the bubble. With this info should finally be able to again read and answer email on any iOS device and still control, have a history, and do longer answers from the computer.

Thanks for a clear answer and not a bunch of crud.
Happy Holidays.
[doublepost=1466453902][/doublepost]I think I've read every possible way that email could ever be handled except the problem I'm having!
How do I KEEP all of my Organized Folders with all of my READ Emails I've saved over the past 20 years "back in the day when there were NO iPhones",,,,, How do I keep all of the old saved emails & the new ones I mean everything on the server,,,,,, and also view the most resent new emails on my iPhone. I'm not talking about DELETED MAIL,,, "even though it would be nice to delete on iPhone & have it gone on the server" but I'm not worried about any deleted Msgs or where they might be & not be,,, I'm worried about all of the mail I've saved over the years That have Pics & Videos that are important to me! Thank you soooo much'
 
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