Whoever catches one rakah of the Asr prayer before the sun sets has caught it. This is reported from Ibn Abbas, from Abu Hurairah, from the Prophet ﷺ. And whoever catches one rakah of the Fajr prayer before the sun rises has caught it.
حدثنا إبراهيم بن خالد حدثنا رباح عن معمر عن ابن طاوس عن أبيه
من أدرك من العصر ركعة قبل أن تغرب الشمس فقد أدركها يروى ذلك عن ابن عباس عن أبي هريرة عن النبي ﷺ ومن أدرك من الفجر ركعة قبل أن تطلع الشمس فقد أدركها
Its isnad is sahih, and it is a narration of one companion from another companion, Ibn Abbas from Abu Hurairah. Muslim likewise related it, 1:169, through Abdullah bin Mubarak, and through Mutamir, who is Ibn Sulayman, both of them from Mamar, with this isnad. Its meaning has already appeared repeatedly, from the narration of Abu Salama bin Abdul-Rahman, from Abu Hurairah, 7282, 7451, 7453, 7529.