Send, Forward, Signatures for 2nd Exchange Account

We have a need to have a couple of users to 'share' a second Exchange email account.  They will each retain their primary personal account but need to read and send email from this second account and see what each of them have said in replies.

I have added the two users with full access and send as rights to the shared account through the Exchange console.  The account automatically adds to their Outlook profile and they can read, more and send email.  However, if they reply, the reply to a message it appropriately comes from the shared account.  However the reply is placed in their personal Sent folder, not the shared email account's sent folder.  I also try to create a unique Signature for the shared account but the only choice for signatures for the individual users are their personal accounts.  The shared account does not show  in the Account Name pull down in the Signature creation window.

I then removed the users from Full Access and Send As through the Exchange console.  I added the rights back in using command lines and disabling the automapping in Exchange 2010.  I then added the shared account into their Exchange profile using the Advanced -> Open Additional Mailbox.  I had the same issues.

I understand that there may be issues if I try to add the shared account as a second Exchange account through Outlook Profile, but I do not seem to have another option.

Is there another way to let these users have the desired functionality:
 
- Read incoming email to the shared account
- Reply to the shared email and have the reply land in the shared email's Sent folder
- Have signature that is applied to the shared email folder independent of which user is sending out the shared email.

Thanks

We are using Exchange 2010 on an SBS 2011 server.