This is awkward. Facebook has sort of confirmed that links sent through private messages on their network adds to the share count on that web page publicly.
This number is added the counter along with the Like button. So, in a way you are ending up adding to the likes that web page has received.
Thankfully, your share is not counted as a Like itself so it does not appear in your or your friend’s newsfeed.
But still… a private share is a private share and to add that to the Like counter is just resulting in an inflated figure. I might share a link privately with negative comments about it. That process should not increase the ‘LIKE’ counter on that web page!