Cannot move e-mails to saved folders in Apple Mail app on iPhone and iPad.

Hello. I have my e-mail accounts (personal G-Mail, business Office 365, etc.) loaded into my Apple Mail account. I utilize the Mail app on all my devices to access and manage e-mails. Several months ago, suddenly I lost the ability to save e-mails from my personal G-Mail account into another account such as my Office 365 work account. For example, if I receive a business e-mail to my personal account and would like to save into a business folder, when I attempt to move it, after clicking the “Move” button, it takes you to the folders area. If you click back to go to another account, the other account is greyed out.

Interestingly, I have no problem saving to other accounts on my MacBook Pro. Only on the iPhone and iPad.

Thanks in advance to anyone who knows what to do.