Can a graduate from university of applied science In Finland study higher degrees (Masters and PhD ) outside Finland? Can a graduate from university of applied science in Finland study higher degrees (Masters and PhD) outside Finland? 
I know you that can do a Masters inside Finland in any university of applied science inside Finland. But I don't know about PhD,
and I also don't know about completing a Masters and PhD outside of Finland. Is it possible?
Yes you can. 
You would have to go through the application process of whichever university outside of Finland that you wanted to apply for. The university may have certain minimum requirements, and it would be a competitive process, with you competing with others trying to get into the university.
Depending on which country and university you choose, you may be counted as a EU student or as an international student, which usually has higher fees than domestic.