after the access on CCCH and moved to the dedicated channel, the first message sent by the mobile is a SABM with:
– Location Update Request
– CM Service Request
In both cases the mobile identity is present there.
This message is sent back by UA and received by the mobile.
If a second mobile was involved in that access, at that point it can stop and move away.
You can find details here:
3GPP 44.018, par. 3.1.5