Transferring emails to a new S6

I have a bunch of work emails on my old phone that I want to put on my new phone but do not have access to the email server anymore. Is there a way to transfer emails to a new phone? Smartswitch and other transfer apps don't seem to move emails. The emails are sitting in my old work email account which annoyingly keeps trying to connect to the server but I really need these emails on my phone for reference. Any suggestions?

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