Hi @Anonymous ,
The following processes will work:
1. Create a Parent Power automate
2. Create a Child Power automate with "Run only users" as one of admin or service user account who has permission "Send-As" for the Shared Mailbox

3. Call the Parent Power automate from the PowerApps as invoking user permission
4. The Parent Power automate will call the Child Power automate. Since it has "Run only users" as one of admin or service user account's connection, it can be generated an email notification from the Shared Mailbox
Hope this helps. Thanks!
Best regards,
Jisung Han