Can a broker trade your money without receiving the signed DOD declaration

Hi everyone,
I need some advice.
can a broker trade your money without me signing for the transfer declaration for money laundering. I didnt think they could but they have traded anyway. Now I have asked for my money back after they bought BTC and lost me $2300 they are insisting on this signed document.
Can anyone help answer this for me ?

Thanks in advance

Had you actually put money into the account or already authorised the transfer?