How can you view who sent a message with "Send As" permissions on a shared mailbox?

It's possible that Filecats Professional can help. Assuming the email is in Microsoft Outlook, if you drag it to Windows Explorer, it is able to analyse the metadata contained in the email and give you a lot of information (see the link for information). I note that this information includes Sender [address] and Sent Representing  [address], so hopefully one of those will give you the information you request.

If the email is not in Microsoft Outlook, then please be a bit more specific.

We are running Exchange 2010 SP3.

sure.

exchange 2010 sp3 by default do not audit such.
you need to enable them manually as below
set-mailbox <sharedmailbox> -auditadmin sendas -auditdelegate sendas

to search them run,
search-mailboxauditlog <sharedmailbox> -showdetails

Again, if you need to audit more detail, you can as well, read the below for details example.
http://www.msexchange.org/articles-tutorials/exchange-server-2010/compliance-policies-archiving/auditing-mailbox-access.html

I've requested that this question be deleted for the following reason:

Never mind I got the answer from another source.