SMTP setting for a Google Group

We use GSUITE and want to use the GSUITE SMTP server instead of SendGrid. We’ve implemented this for support@… and this works because this is a primary user in GSUITE and we use this mailbox. However, for Google Groups we don’t have a primary mailbox and if I use the SMTP settings of support@… then the mail isn’t send with the common groups address but with support@… How can we solve this? Thanks in advance for your help,