I haven’t done this myself, but I’ll chip in and offer some advice.
From my understanding, to use the same email address (I assume it uses the same domain as their website), then this will be something to do with the domain control panel. Related to MX records and SPF/TXT records. A quick Google will help you with this.
As for moving data and everything over from Office365, I found these two articles that might be helpful:
https://support.google.com/a/answer/6251069?hl=en
https://spinbackup.com/blog/migrating-from-office-365-to-g-suite/
Let me know if this is what you are looking for. If you have any further questions, just ask.