How do I exit private browsing mode in iOS but retain all of my private tabs?
As of iOS 12 beta 2 and below, this is not currently possible with Safari.

As said by @Snowbody,


  [You can copy &amp; paste] all the URLs from the URL bar into an email or other document[.] Of
  course that doesn't preserve history, form fills, etc.


Your best option is to either find a different browser with that feature (maybe create a new question) or to submit a feature request to Apple.