Cant help with blackthorn but with Rosa Rugosa I first dig around a well developed sucker to see if it has developed a good root as some suckers are just underground branches and then chop off as near as the main plant as poss and replant the whole underground bit. I do this in spring with Rosa but dont know about Blackthorn, the reason being the plant will be going dormant shortly, in spring the plant will be kicking into gear and develop better. Thats what I do anyway and it works