Issue: Your O365 hosted email bounces back as SPAM from any g-mail/google hosted domain.
SOLUTION: Create a DMARC record for your domain
The "TRUE" solution is to add a DMARC record to your domains DNS records. I won't go into details of what dmarc is, but you can read it here: https://dmarc.org/ . The simplified version is that "YOU" are sent reports by ISPs regarding how your domain name is being used.
**If you do not know how to add a record into your DNS server, contact the person who manages it for you".
The record is very easy to build. It requires sending to an valid email address. I strongly recommend creating "THIS/AN" special email address (a group based distribution list that can receive email from outside your org). I use dmarc@ for all my domains email.
The format in DNS is as follows
HOST: _dmarc
VALUE: v=DMARC1; p=none; rua=mailto:YourEmailAddress; ruf=mailto:YourEmailAddress; fo=1:d:s
TTL: I prefer 1Hour but you can choose anything.
Once it is set up correctly, you can test this by going to https://mx****/dmarc.aspx
That is all there is too it. No need for special mail flow rules.
Michael B. Morell, CISSP #431307 CCSK
Information Security