On-premises mailbox permissions such as Send As, Receive As, and Full Access that are explicitly applied on the mailbox are ...

On-premises mailbox permissions such as Send As, Receive As, and Full Access that are explicitly applied on the mailbox are migrated to %BRAND_EXCHANGE_ONLINE_SHORT% Online in %BRAND_OFFICE_365_SHORT%. Inherited (non-explicit) mailbox permissions and any permissions on non-mailbox objects—such as distribution lists or a mail-enabled user—are not migrated. Therefore, you have to plan for configuring these permissions in %BRAND_OFFICE_365_SHORT% if applicable for your organization. For example, you can use the Add-RecipientPermission and Add-MailboxPermission %BRAND_WINDOWS_SHORT% PowerShell cmdlets to set the permissions in %BRAND_OFFICE_365_SHORT%. Learn more at Permissions in %BRAND_EXCHANGE_ONLINE_SHORT% hybrid deployments.