Yes, I can help with that.
Short answer: the issue is that during a warm transfer, the transfer assistant usually does not receive session variables like {{first_name}}, {{last_name}}, or {{customer.number}} it only gets the conversation context, not dynamic variables.
A quick question to clarify so I can guide you properly:
What platform are you using for the calls (e.g. Twilio, Amazon Connect, Genesys, etc.)?