the part should be in one piece, with no splits
reason for the split might be an incorrect installation introducing the part through the hole as it is now everything mounted in the car
how should the part be installed, well, you should put down the gear box so you would be able to insert the foam part through the gear box lever and then up again, pretty major work for what you intend to do
if the foam is disintegrated and you want to replace it you might try with the gear box in place, you produce a cut in the new foam part and you introduce it through the hole, prior to this remove as much as possible of the actual foam using your fingers to pry it up or to push it down
IMHO, if you place the split rearwards and if you use a new part foam intact, there is not a very big difference with the correct insertion of the complete part,
...another question is if that is really the source of your problems, have you checked that is really the entrance of hot air while driving ?