To share a connection means to have something in common or a mutual understanding or bond with someone. It implies that there is a sense of connection or relationship between two or more people. Full definition
Users can make connections, network, share their connections with friends, search users by name, location, profession, and more. (creditdonkey.com)
Somehow, I think they will draw the line at groups of unrelated persons sharing the connection in a neighborhood. (legalblogwatch.typepad.com)
I knew I had to share the connection between health and nutrition so people could take their well - being into their own hands before it was too late. (nutriplanet.org)