https://wiki.zimbra.com/wiki/Ajcody-How-To-Setup-sendAs-Right-And-Persona-For-Internal-Users

Use the Zimbra Admin 'gear icon' to show options.

1. Configure → Domains → Add a Domain Alias (if any)
2. Manage → Accounts → Aliases → Add → Save
3. Manage → Accounts → General → Edit Account → Delegated Authority → Address Delegation → Allow → Save

To grant the right to a user account:

su - zimbra
zmprov grr dl list@example.tld usr user@example.tld sendAsDistList

To revoke the right:

su - zimbra
zmprov rvr dl list@example.tld usr user@example.tld sendAsDistList