Hello Morningstar247,
As far as I know roundcube web email is a third-party email system, if so, as far as I know you could configure the roundcube email account to Outlook Client as IMAP, after that use Outlook Client to export all the emails to a pst file, then if you have your own Microsoft 365 Business mailbox, you could import the pst file into your Microsoft 365 mailbox to access the emails. Also if you have your owned custom domain set up with roundcube, after successfully migrate the emails to Microsoft 365, you could also change the DNS records of custom domain to Microsoft 365 and then send/receive emails in Microsoft 365 mailbox directly, thanks. For your reference add an email account to Outlook. And mport and export Outlook
Please note to add your roundcube web email account to Outlook, you need manually configure the email accounts with incoming/outgoing server addresses and ports etc. If you don't know about it, please contact roundcube tech support for further assistance, thanks.
Please feel free to let me know if you need any further help regarding Microsoft 365, thanks.
Best Regards,
Oliver
