According to Quirk, it is possible to view each situation as unexpected in the light of the other and therefore to choose which should be made subordinate:

For example: No goals were scored, ALTHOUGH IT WAS AN EXCITING GAME.
It was an exciting game, ALTHOUGH NO GOALS WERE SCORED.

ALTHOUGH IT RAINED ALL DAY , we enjoyed ourselves.
ALTHOUGH WE ENJOYED OURSELVES, it rained all day.

Is it possible to move the conjunction "although" as it is shown in the examples? Is it grammatically correct?

Yes, grammatically correct, but changes the meaning/emphases of your sentence. You are changing the subject of your sentences.