Dear Rima,
Good day! Thank you for contacting the Microsoft Community. We are here to assist you
It seems like you're experiencing an issue with syncing Microsoft Forms responses to Excel when the form is owned by a SharePoint group.
Technically, if you move the form to a new or existing group it give all group members full editing capabilities. And they can follow the steps mentioned in Update to the new solution for syncing forms responses to Excel.
If you already tried the steps mentioned in above article and the issue did not resolve, the configuration of your tenant need to be checked with help of a specific team at Microsoft. Therefore, I recommend reaching out to the relevant product team for assistance. This can only be initiated by an Office 365 Global Administrator. The Microsoft Support Team has higher permission to remotely assist you and collect background logs for the root cause. This is a more efficient way in handling this case for you.
If you are an admin, I recommend you get support by following steps from this link: Get support - Microsoft 365 admin | Microsoft Learn. If you are not an admin, you can contact your admin to contact Microsoft support. You can look for the way to find your admin through this link: How do I find my Microsoft 365 admin? - Microsoft Support.
Meanwhile, you can try temporary work around mentioned in Create an automated workflow for Microsoft Forms to check whether it resolve the issue.
Please accept my apologies for redirecting you to the related team support, as the moderators in this community have limited resources and permission to verify the backend information and to get the quick and better assistance, we requested for this.
Have a great day and take care! 😊
Sincerely,
Naren | Microsoft Community Moderator