Is there a way to send an entire IMessage conversation trough email?

There is no direct method available on the iPhone to send an entire Message thread via email with one or two clicks. The available methods are The Copy/Paste method or Taking ScreenShots and then attaching those to emails.

There may be other third party apps available for a computer to do what you are asking for. Perform a Google search on the internet and see if there are apps available for this. I have no such experience.

Axel F.