Is the prayer valid when Surat Al-Fatiha is recited therein without a prior intention, given that there was an intention for the prayer at its beginning?

The cure for obsessive thoughts is to ignore them and pay them no mind. It is sufficient to bring to mind the intention of prayer when commencing it. The prayer is not invalidated by not bringing to mind the intention to recite Al-Fatiha, nor by hesitation concerning it, as long as its recitation is correct.