Yes - you must still register this work within your own Songtrust account, regardless if it has already been registered in another ST account. When we send out songs for registration, it is not only to just register the song with PROs, but also to claim it as your publishing administrator so we can begin collecting royalties for the work on your behalf. If you do not add the song into your Songtrust account, there is no way for us to know that we need to claim it on your behalf. Just because your co-writer registered this work in their account, it does not always mean that the other co-writers also want us to administer their shares. So, if you also want us to claim the work on behalf of yourself, you must add it into your own account.
When you add this song into your account, make sure to add your co-writer as an OUTSIDE writer. Even though they are also with Songtrust, they are not a songwriter within your own account - so they are still considered an outside writer for registration purposes.