Access your gmail account the way you always do, click in the cogwheel in the superior right side and then Settings.
Click over the tab Accounts and Import and search for the option Add a POP3 mail account you own and click.
Type in your professional webmail account and click on Next.
In username type in your whole e-mail address again, then your password as POP server and click on add account.
Chek the option, Yes, I want to send… and click on Next Step.
Select a name for your webmail account and turn off the option Treat as an alias, and then click on Next Step.
Make sure the option send with Gmail is selected and then click on Next Step.
On the next window click on Send Verification, once is done, in another tab of your navigator, go to your webmail inbox.
Finally, you should have received an e-mail with a number, copy and paste it into the box that appears and then click on Verify, then it should be done and you will be able to send and receive e-mails from your professional webmail from your Gmail.