If you wanted to delegate permission to a user or a set of users for multi-mailbox search, you may add them to the Discovery Management RBAC role group, which contains two management roles. 1. Mailbox Search Role and 2. Legal Hold Role. By default this role group does not contain any members, that means none of the users including the Exchange Organization administrators do not have permission to perform the Multi-Mailbox search. However, the Exchange Administrators who are member of Organization Management role group can add users into the Discovery Management role group to perform the multi mailbox search.
Once the user is added to the Discovery Management role group, those can perform the multi-mailbox search using the Exchange Control Panel. Below screen shot shows a typical Multi-Mailbox Search window. Once you have entered the required information on New Mailbox Search, click on 'Save' button at the bottom of the window, that's all.
More details on how to add users into the Discovery management role group and do a mutli-mailbox search will be published on my upcoming posts.