A friends business email goes through to his gmail account, but he also pays for an email account with his web host. Is it necessary to keep paying for this email account, does he need it if the email goes through to gmail?

EDIT: What I know is, they both receive and send emails from @theirdomain.com via their Gmail. They have their domain registered with a seperate company than the web host and have access to their DNS records there. With the hosting company they pay for email in addition to their hosting plan.

My friend wants to avoid the extra cost of the email account if possible, and I thought it wasn't required to have an email with your your webhost if setting up the DNS records properly, but not 100% sure. We wanted to get independent advice before proceeding, since the host has an incentive for my friend to stay on the email plan.