I'm not 100% sure if you're trying to have all of your email on Sonic or on Gmail's side. I might be misunderstanding what you want, but I would suggest having your Sonic account forward to your Gmail account. Once you do that, follow the steps below to be able to respond from the email address that the email was sent to. Excuse my censoring for privacy, hopefully this makes sense.
1. First step, go to
settings
2. Then to
Accounts and Import tab
3. Next to"Send mail as:" you may have your Sonic email address. If you do, you need to delete it. If you don't, skip to step 4.
4. Now, it's time to add your Sonic email. Select
Add another email address you own under "Send mail as."
5. On the first page, put in your name (as you want it to appear) and your Sonic email address, then click
Next
6. The Sonic SMTP server is mail.sonic.net. The username is your Sonic email address in full. Also put in your current Sonic email password. Use Port 587 and TLS. Click
Add Account.
7. Gmail will send an email to your Sonic address with a code. If you're already forwarding it to your Gmail account, then it be in your Gmail inbox, otherwise check for the email
https://webmail.sonic.net. Copy and paste the code Gmail sent into the confirmation code box and click
Verify.
8. Now you should be back at the Gmail
Settings->Accounts and Import window. Under
Send mail as you'll want to check a few options. In my case, I use my Sonic email as a secondary account so I leave my Gmail as my default address. If you want to send from your Sonic account by default on new emails, click
make default next to your Sonic account. You usually want to check that
Reply from the same address the message was sent to option. Also, here you can see that it'll use Sonic's server for your outgoing email.
9. At this point, if you haven't yet, you'll want to set your Sonic email to forward to your Gmail address. You can do that forwarding at
https://members.sonic.net. You now have a single inbox for both your Gmail and Sonic accounts.
You can also use the Gmail apps on your mobile device as well, if you want to. I hope that helps!