Is it possible, for a user, to connect to several organizations ?
You will not be able to use the same user for several organizations. For example, your user account cannot be a user/publisher/administrator in another Organization.
However, many organizations can invite your user to their Groups. For example, if my user is 'jskinner' and belongs to the Esri Philadelphia Org, this user can be invited to any group in any organization. The user will then have the ability to view/share any data to this group.
Thanks for your answer
When I search a user for invite him to participate to one of my groups, I can't find him.
What conditions must have a profile to be found ?
The user will need to go to their profile in ArcGIS.com and check that the 'Everyone' can see their profile.
Retrieving data ...