Our group arrives via United Airlines in PEK T3 then departs via Mongolian Airlines in T3

According to your situation, it is an international to international transfer both in T3. Thus the transfer time is enough. Don't worry.
Hereunder is the transfer procedures:
Flight Arrival - Transfer Procedures - Border Inspection - Security Check - Custom Inspection - Waiting & Boarding

Hope helpful!

My question is the transfer procedure. Do you have to fill out any special forms like when transferring from terminal to terminal? Or do you simply go through the gates to the left of the passport entry
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Thank you,
Robison

Don’t worry about your transfer and just follow the transfer procedures I told you. You needn’t fill any special forms and just need sign you name to ensure your belongings in Transfer Procedure.