Assign request to email in "To" field

Assign request to email in "To" field

Good day

I still receive support mails to my personal address and I'd like to reply to the person and cc my support address. However when doing this, the request is linked to me, not the person I'm responding to.

Basically, I want to build a workflow as follows:

Mail received from person@example.com in Outlook.
I reply from me@mycompany.com and cc support@mycompany.com
Support picks up the mail but assigns the request to the person I reply to (person@company.com) and not to me (me@mycompany.com)

Is this possible?

Thanks