If the fire alarm wasn't common to all occupancies then I wouldn't be able to see why a landlord fire risk assessment might be required. However, if the landlord doesn't look after the fire alarm system then there might be a possibility that people are put at risk in the building. I say 'might be a possibility' because I do not know how beneficial the fire alarm system is to the tenants (i.e. it might not be required for life safety, it might only be for property protection).
The tenants do all have to do their own FRAs, of course, and I would recommend doing one for the landlord that covers: a) the fire alarm system, and b) the common areas immediately outside the exits from the building (for example, these might need emergency lighting or they may have uneven surfaces - ok, probably not, but you have to make the trip worthwhile).
stu