Official policy as it was published in 2017. My bolding to direct readers to the most commonly asked part. Do note wording 'allow'.


THROUGH CHECK-IN POLICY
Finnair takes care of passenger’s through check-in in all cases where the passenger has an agreement of carriage with Finnair and the through check-in is technically possible and is according to local instructions. This agreement of carriage requires that the passenger holds a Passenger Ticket and Baggage Check, or an electronic ticket, as defined in the Conditions of Carriage and issued by Finnair or on its behalf.
Passenger’s flight reservation (PNR) and flight ticket (single agreement with specific airline) are not always the same thing. Each ticket with different ticket number is an independent agreement of carriage with the ticketed air carrier. It is not possible to through check either passenger or baggage between separate flight tickets even if they are in the same PNR. Check-in is possible only to the final destination on each individual agreement of carriage (= flight ticket).
It’s important to remember that MCT (Minimum Connection Time) at each airport is based on the assumption that flights are booked on the same ticket and this way passenger and baggage may be through checked to the final destination. In case flights are on separate tickets, passenger has to collect baggage and recheck on the connecting flight at the transfer station thus MCT is no longer valid. Passenger shall be informed already at the time of reservation that check-in can be done only as far as Finnair has a contract of carriage with the passenger.

FINNAIR THROUGH CHECK-IN POLICY
Passenger and baggage shall be through checked to the final destination as indicated by the flight ticket, provided it constitutes one single agreement of carriage with Finnair. Finnair will provide through check-in for a journey ticketed in a single PNR; this includes segments ticketed separately but booked in the same PNR (and/or referenced in a single PNR during the time of booking).

In addition to the basic rule Finnair will allow through check-in of customer and baggage with separate tickets on separate PNRs on AY–AY (including AY franchising flights operated by Norra) connections when the transfer is within the Minimum Connection Time (MCT). For AY–AY connection flights on the separate PNRs have to be both marketed and operated by Finnair or Norra and flights ticketed on the 105-stock. The agent shall always inform the customer of the destination where the customer and his or her baggage are checked-in to.