contact forms that work with offfsite email like office365

Hi,

I want to be able to find a contact us form that will email the submissions to an outlook/office365 offsite hosted email. I haven’t had any luck with “contact form to email” and it doesn’t send emails to my domain which is on o365/outlook. Is there a contact to email form that works or do I HAVE to use the same email hosting as the same server as WP is on? That would suck since I prefer to have email externally hosted so I can still use it if my own server is down.