H1B Transfer without a client letter

One employer has offered me to transfer my H1B, however not arranging a client interview and “Client Letter”. I have been asked to pay the premium processing fee and “Security Deposit”. I am apprehensive about getting H1B stamped without Client Letter, and have raised my concern with employer, however employer is saying their attorney will take care of everything even if there is any RFE. The employer’s feedback on internet is positive however the case I mentioned seems suspicious to me.
I am still in doubt, is there any possibility of getting stamping done without “Client Letter”?

Should I trust them and pay the money as they say?