Fan extractor handyman help

Hi all

Recently moved into a flat that has a recirculating fan above the hob, one of those with a charcoal filter that does't really do anything to remove cooking odours. Recirculating fans - what's the point?

Anyways, literally 1 meter away is a hole designed to extract the air outside. I've asked the landlord if they'll deal with it but have gotten a tepid response, so looking for some help in getting this done myself.

Would you know how much connecting the fan to the wall costs and recommend someone who has done this type of job?