Is it permissible to recite the 3 Qoels I’m the fard salaah in one rakaah without saying the basmalah when finishing the one surah and immediately start the next one?
It is permissible to do so. Salaat will still be valid. However, one should try his best to recite the basmalah silently before each Sura. (Kitabul Fatawa vol.2 pg.396)
And Allah knows best,
Mufti Waseem Khan