AWS to GMAIL forwarding - send and receive mail from domain email?

I want to configure my AWS SES to be able to achieve the following: i want to be able to send an email to a@example.com and i want to be able to view it when i log into example@gmail.com. when on gmail, i want to send an emails via a@example.com.

I want to use gmail as the interface. also be able to do the same thing with info@example.com, where it will also be forwarded to example@gmail.com and i have already set it up so gmail filters the "to(a@example.com)" and "to(info@example.com)"

if it helps, i already have this configured with hostgator (cpanel) using their email forwarding and email accounts.