Hi Gallini
You will either have to ring the DWP to ask or wait for the letter to arrive. I expect you will receive the letter within the week. The assessor who told you it would be weeks is not the person who makes the decision or activates any monies due. I'm glad that it appears to have happened to you so quickly. It does sometimes - but not nearly often enough - so I'm happy for you.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems 
