HR asked me to confirm if the HR team of my previous organization would cooperate for background verification

I recently got a new offer and have accepted it. I am a fresher and this is my first job switch.

My resignation from my previous organization was accepted. When I submitted the acceptance email to my next company they asked me to confirm if the HR team of my previous organization would cooperate for background verification.

I am not sure how the communication between the two companies is in India. My questions are:
1. What should I reply to my new company now?
2. In the future, if my previous company does not cooperate with the BGV what should I do?
3. Is there any rule for the previous companies to cooperate with the new companies regarding their employees' BGV?

Thanks in advance!