If you are using Proofpoint for outbound messages, you will need to add an additional Routing Rule, so the Notification of the Shared Document does not get Routed via Proofpoint.
If you do not add the additional Routing Rule the notification to External recipients will not be delivered.
Please follow the below steps to add the Routing Rule.
- Go to https://admin.google.com
- From the dashboard go to Apps > Google Workspace > Gmail >Routing.
https://admin.google.com/u/0/ac/apps/gmail/routing
Click Add Another Rule

Add a name like Google Doc
Select Outbound

Scroll Down to Route.
Click Change Route.
Dropdown Select Normal Routing.

Scroll Down and Click Show more options

Scroll to Accounts to Affect and select Users and Groups.

Scroll Down to Envelope Filter.
Click Only affect specific envelope senders.
Select Single Email Address from the Dropdown.
Enter the following email address.
drive-shares-dm-noreply@google.com

Click Save at the bottom right corner.
This Rule will not Route the notifications to external recipients via Proofpoint.