Yes, you can! This assumes you are forwarding your UCSB Umail to your UCSB Connect/Gmail account.
Your UCSB Google account is branded as "Connect".
Do the following -
- Login to your U-Mail account @ https://umail.ucsb.edu UCSBnetID@umail.ucsb.edu (this is office 365).
- Login to your UCSB Gmail/Connect account - https://gmail.com with UCSBnetID@ucsb.edu
- From your Gmail/Connect Account go to Gear Icon (upper right) -> Settings -> Accounts
- Add another email address (UCSBnetID@umail.ucsb.edu) and check the treat as an alias checkbox.
- Click Next Step
- Click Send Verification
- Wait a minute or two
- Go to your Office 365 account, refresh your email, find and click the verification link in the email message.
- Go back to your Connect/Gmail Account in "Settings -> Accounts" and make sure in the section "When replying to a message:" it is set to "Reply from the same address the message was sent to"
If you want to test this, you can send a message to your U-Mail account from your personal email, then read it and reply from your Google Account. MEssages forwarded from U-Mail to Google might take an extra few minutes.