I have copied my email and encryption files to a new Ubuntu installation as follows:
Exported GnuPG keys from old desktop and imported on new one. (And other passwords and keys.)
Opened Evolution on the old desktop, selected
File > Back up Evolution Data.... Copied the file across. Opened Evolution on the new desktop, selectedFile > Restore Evolution Data...Confirmed on the new desktop that:
The OpenPGP Key ID appears under the Security tab in the Evolution Account Editor (matches old desktop)
The GPG keys appears in GNOME Passwords and Keys (aka Seahorse)
However, when I attempt to read encrypted emails on the new desktop, Evolution cannot open them. It says "Could not parse PGP/MIME message: Failed to decrypt MIME part: Secret key not found". This applies to new encrypted emails and old ones, including those sent by me.
I also cannot send signed or encrypted emails. When I try, it says "Could not create message. Because: 'gpg: skipped '12345678': No secret key. gpg: signing failed: No secret key', you may need to select different mail options."