I would like to change a current members email address without losing prior activity.

[Wayne Desmond]

I would like to change a current members email address without losing her previous activity.

Is this possible?

[Michael Pryor]

If the user themselves log into their account and changes their email address, no previous activity will be lost.  You can't change another account's email address though.

You can invite a different email to the board (and remove the original) but it won't do what you want (It will treat that new email as a new account).

[Ali Banaee]

I have a similar question here, would you mind taking a look at it?
https://community.atlassian.com/t5/Trello-questions/Changing-email-address-and-keeping-history-of-original-account/qaq-p/1904913#M56890