VAT between legal entities from different countries

Question:

A Romanian SRL (a limited liability company) tax registered and for VAT purposes in Romania charges a Government Nonprofit Organization (NGO), a non-VAT payer in Germany for training services provided in Finland (for this NGO). The invoice contains training services, material preparation and other costs. The courses are held in Finland, the NGO charging fees, the fee for students or other participants who can be from anywhere in Europe. Does the Romanian VAT company, SRL, collect VAT to the invoice issued to the NGO and should register in Finland for VAT purposes?