Caliming HRA for portion of a year

I stayed in 2 rented houses , one from Apr-2022 to Oct-2022 and another from Nov-2022 to March-2023

I had to shift house because of job change and HRA and Basic component of these 2 jobs are also different.

But in the new house owner is not giving his PAN details , but owner from old house used to give PAN.Because of this confusion I didnt claim any HRA from my new employer.

So I am planning to claim HRA only for Apr-2022 to Oct-2022 during IT returns filing.

AFAIK , I need to consider basic/HRA from my payslip for Apr-2022 to Oct-2022 and also rent for same period while calculating HRA exemption. Is that right?

If it is correct how do I give the details of this methodology of calculating HRA exemption in ITR-2 or inform Income Tax office about this? ITR-2 asks only for final exemption amount.

Can I just claim now and worry about it when I am asked to give more details of HRA exemption?

Thanks!