Microsoft source: here
This configuration enables users to reset their own password and have them synced back to the on-premises Active directory.
Permissions for cloud sync are configured by default.
This permission is configured by default as well.
When this option is enable, users who change or reset their password have that updated password synchronized back to the on-premises AD DS environment as well. To verify and enable password writeback in SSPR:
Edit the GPO for Minimum password age from 1 to 0. This would allow users to be able to reset their passowrd as many times in a day.
One of the benefits of using Entra Connect Cloud Sync over Entra Connect Sync is that group ManagedSservice Account(gMSA) should have the following permissions set to writeback the passwords by default.
If these permissions aren’t set, you can set the PasswordWriteBack permission on the service account by using the Set-AADCloudSyncPermissions cmdlet and on-premises enterprise administrator credentials:
Import-Module ‘C:\Program Files\Microsoft Azure AD Connect Provisioning Agent\Microsoft.CloudSync.Powershell.dll’ Set-AADCloudSyncPermissions -PermissionType PasswordWriteBack -EACredential $(Get-Credential)
Also, you can manually set those permissions on AD. Login to AD > Managed Service Accounts OU > Right-click on provAgentgMSA > Properties > Secutiy > Advanced Click on Add.
NOTE: For passwords to be changed immediately, Minimum password age must be set to 0
https://learn.microsoft.com/en-us/entra/identity/authentication/tutorial-enable-sspr-writeback#configure-password-writeback