This worked for me and seemed a lot easier as it requires a not so fine movement: once you unscrew the fan, don't remove it entirely; just pull it up enough so you have space to insert the new one but without having to remove it from the black tape. Install the new fan and the two screws and then, pull the old fan down and towards you slowly and as horizontal as you can; if you do it like this the same movement of removing the tape will also place it over the new fan, and in it's natural position. Then just a press with the finger to firmly stick it to the new fan and you are done!

The screws have to unscrewing positions, first they unscrew from the whole body BUT if you move the lid without entirely removing the screws, they will remain attached to the lid. This I find much more recomendable!