LHA: is there still 13 weeks or 52 weeks protection for specific groups?

Son was living with father who was the tenant. Father has died and son has new tenancy of same property. The rent increased when son became the tenant and rent is now well above LHA.  Son wants to make a new claim for HB.

I am correct in assuming son won’t get any protection and LHA rate will apply?  Would it make a difference regarding protection if the rent had remained the same?

Or if father (claimant/tenant) was still alive but someone else in the household had died, is that when the 52 weeks protection would apply?

If son won’t get protection but was initially able to afford rent of new tenancy but subsequently lost job etc., is that when 13 weeks protection would apply?

Thanks

As I understand it, “if the claimant was on HB at the date of the death” of the ‘linked person’ (in this case the father), “their eligible rent must not be reduced to below whatever was their eligible rent immediately before that date.  If the claimant was not on HB at the date of death, their eligible rent is worked out in the same way as in a standard case…..and cannot be restricted in anyway”  (Shelter Guide to HB/CTB, paras 9.75, 9.76).  As the claimant was not on HB at the date of death, then I think the 52-week protection applies, and the eligible rent worked out as in a “standard case”, i.e. actual rent minus ineligible charges, without restriction. 

Maybe a HB specialist could confirm or not…

Thank you very much for your replies and for explaining in such detail