Mould - caused by condensation or not ?

Hi , I have a very long standing tenant in a room ( not ensuite ) in an HMO who tells me that she keeps her room well ventilated but there is still mould occurring . She is convinced that its caused by damp coming through from the outside due to a break in the render. I have had it inspected by a franchisee from Envirovent who says that that its definitely due to condensation as the walls are cold where the mould is apparent. Theres no mould anywhere else in the house. She doesnt accept this opinion!

Has anyone overcome a similar issue ?

Whats the best course of action ? Do I just treat the mould everytime it appears ? I believe theres a product which keeps mould away for 3 months -- can anyone confirm what it is ?

I know one solution would be to fit an extractor fan but dont think its viable as even the quietest ones would disturb.

Or could the tenant be right ? and is there a building solution to this ?

Thanks for any help . Glenn