Hadith: Whoever catches one Rak‘ah before sunrise, he has caught the Fajr prayer, and whoever catches one Rak‘ah of the ‘Asr prayer before sunset, he has caught the ‘Asr prayer

عن أبي هريرة رضي الله عنه أن رسول الله صلى الله عليه وسلم قال:«مَنْ أَدْرَكَ مِن الصُّبح ركعة قبل أن تَطْلُعَ الشمس فقد أَدْرَكَ الصُّبح، ومن أَدْرَكَ ركعة من العصر قبل أن تَغْرُبَ الشمس فقد أَدْرَكَ العصر».
[صحيح] - [متفق عليه]

Abu Hurayrah (may Allah be pleased with him) reported that the Messenger (may Allah's peace and blessings be upon him) said: "Whoever catches one Rak‘ah before sunrise, he has caught the Fajr prayer, and whoever catches one Rak‘ah of the ‘Asr prayer before sunset, he has caught the ‘Asr prayer."
[Authentic hadith] - [Narrated by Bukhari & Muslim]

Explanation

The Prophet (may Allah's peace and blessings be upon him) informs his nation about the final time of the Fajr and the ‘Asr prayers. He stated that whoever catches one Rak‘ah, meaning: he prays one Rak‘ah and raises up from the Rukū‘ in the Fajr prayer before the sun rises, then he has performed the morning prayer in its due time. Similarly, whoever catches one Rak‘ah of the ‘Asr prayer before the sun sets, then he has performed the ‘Asr prayer at its due time, because one Rak‘ah of the prayer has been performed within the prescribed time.