According to a site whose name is "Muscles of Iron", the above picture shows Lincoln after taking down “champion” Jack Armstrong at the general store in New Salem, 1831.
On the page where the picture is shown, it is written:
But, before anybody could take Lincoln up on his offer, Jack Armstrong yelled out, “Boys, Abe Lincoln is the best fellow that ever broke into this settlement. He shall be one of us.” Then, with a touch of dignity and class, Armstrong held his hand out to Lincoln and congratulated him for his victory. This was the beginning of a special friendship between these two powerful men, a friendship that would last until Lincoln’s death.
But, Wikipedia, in reference to that match, says:
His place with them was cemented when he engaged in a wrestling match with a local champion, Jack Armstrong. While Lincoln lost the match, he earned their respect. (My emphasis)
Therefore, since it seems that Wikipedia and Muscles of Irons, which show even a picture, report opposed versions about the result of that match, question is: Is there a reliable source that agrees with "Muscles of Irons"?