Praying Asr Or Fajr Just Before The Time Ends
I think it is permissible to pray Fajr or Asr if you can complete just one rakat before the time ends. This is in accordance with the Hadees that one can complete a Namaz even if the time for it has passed during that Namaz. So if you’ve completed one rakat of Fajr Namaz and it is time for sunrise you can complete that Namaz. Exactly the same for Asr or any other Namaz.