You can add forwarding to an email account where every email that is sent to a particular account is automatically sent to a different one. This applies to all emails however if you want to automatically forward messages from a specific address, but not all of them, Gmail has a built-in tool for the job.
Forward emails from a specific address
Open Gmail and go to a message from the email/sender you want to forward all messages from. Click the more options button (the three dots), and select the ‘Filter messages like these’. In the panel that opens, click the ‘Create Filter’ button.
On the next panel, enable the ‘Forward it to’ option and click ‘add forwarding address’. You will be taken to the settings tab where you can enter an email to forward messages to. Enter one and then access the inbox of the email address you just entered. You will get an email asking to confirm it as a forwarding address. Go ahead and confirm the address and add the filter all over again. This time, the email that you entered and set up as a forwarding address will be listed in the dropdown. Select it, and create the filter.
Any time you want to turn off forwarding for the email address, you’re going to have to go to your Gmail settings. Click the gear icon on the Gmail page and select Settings from the menu. Select the Filters and Blocked addresses tab and remove the filter for the email address.
As for forwarding, when it works it allows the message to arrive in your inbox and you can read it from there. At the same time, the same message is also sent to the address you set up for forwarding. You can read it on either one. If you’d like to disable alerts for messages from that particular email in Gmail, you can add a filter to it that will automatically archive it for you.
This feature seems basic but you’ll find it’s absent even on the best, most powerful desktop email clients. Outlook for one doesn’t seem to have a simple way to forward messages from a particular email address. As for the web interface of other email services, they have a lot of catching up to do even if they don’t add an address-specific forwarding feature.
Remember that if you cannot access the inbox of an email address, and confirm the request to forward emails to it, you cannot set forwarding up. You will have to use a different email address.