Mesmo assim, Search-Mailbox é o caminho a seguir, por favor leia os seguintes dois paráfrases de link :
"The DeleteContent switch specifies that the messages returned by the search be permanently deleted from the source mailbox. When used with the TargetMailbox parameter, messages are copied to the target mailbox and removed from the source mailbox"
"Before you use the DeleteContent switch to delete content, we recommend that you test search parameters by using the LogOnly parameter, as shown in Example 2."
Sugiro que você verifique o link e (possivelmente o ) escreva o seu script atual (s em conformidade)