How should I email a group member from an international group in my area that I previously worked with? I am PhD student in biomedical signal processing area. Before starting my PhD in January 2015, I was researcher in a research group in which I had the opportunity to know one of the best researchers in my area of interest who is also a member of the best group in the world. 
After starting my PhD I decided to continue in the same area but with a different group. Now I want to get in contact with the researcher, I mentioned above, and ask for collaboration. 

What should be the content of my email regarding the researcher's relations with my previous group? Should I explain the about the reason's of changing group or not?
Young students are expected to move around for any number of reasons, so I don't think there is any particular need to explain your reasons for changing groups unless the other person asks.  Instead, I would recommend getting back in touch with a simple greeting and a focus on the new collaboration that you are aiming to establish.  An example of an email along these lines might be:


  Hello, Dr. X:
  
  You may remember me from our previous work when I was studying under Prof. Mysterio.  I am now pursuing my Ph.D. under Prof. Moriarty, working on the same subject of penguin wrangling.  As before, your work on penguin tracking devices would be very useful; would you be interested in continuing our collaboration?


Adjust as appropriate for your particulars.