How to prevent your mail gateways from being blocked due to spam being sent via mail forwarding
Solution 1:
The receiving mail system cannot tell the difference between forwarded spam and real spam. If you forward email, you always have the huge risk of blacklist unless you control the receiving mail system as well.
This happens often with web hosting accounts forwarding the email for a domain to Gmail, Yahoo, Hotmail, Aol, etc. You can either constantly fight the blacklist, or encourage users to take advantage of the POP access of some accounts. Gmail has an easy feature to automatically download email from any POP inbox into your account.
Anyone with a desktop or mobile email client can be downloading the email directly instead of forwarding it. Make sure users know the risks of forwarding, and that you're doing everything you can to keep the system out of blacklists... but that it will very likely continue to happen as long as they're forwarding and getting spam.
If users are forwarding so they have a single web-based inbox and do not currently use a service allowing POP integration, they do have the option of switching to Gmail and using delegation for both of their addresses.