Hi @Georgiev Ventsislav,
Even though each group member has their own mailbox, they all use a shared mailbox as well to receive and manage messages sent to the group. This shared mailbox has a default storage quota of 50GB, and if that limit is exceeded, messages sent to the group will bounce back with the error message you encountered.
To fix this problem, you will need to free up some space in the Microsoft 365 group mailbox by either deleting old or unnecessary emails, or archiving them to another location. You can also implement best practices in managing the Microsoft 365 group mailbox size to avoid it reaching its quota limit in the future.
You can monitor the group mailbox using the PowerShell commands in this article: Microsoft 365 group mailbox size management.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.