That's an Exchange operation, so you need to add the user to the corresponding roles (role groups) in Exchange. Open the EAC > Roles > Admin roles or go directly here:
https://admin.exchange.microsoft.com/#/adminRolesCheck which role group the other user is assigned to, and copy from it. By default, only the Organization Management role group has sufficient permissions to perform this task, so I assume you likely have a custom, more restricted role created to limit the permissions. If needed, consider creating a custom role group with just the "Organization Client Access" role assigned.