Firstly: it is not permissible for a Muslim to forego prayer no matter what the situation. But if he is sick, then he should pray according to what he is able to do. So he should pray standing up; if he cannot do that, then he should pray sitting, and if he cannot do that, then on his side. The evidence for that is:
1 – ‘Imraan ibn Husayn (may Allaah be pleased with him) who said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) said: ‘Pray standing, and if you cannot, then sitting, and if you cannot, then on your side.’” (narrated by al-Bukhaari, 1117)
2 – It was narrated from Jaabir (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said to a sick person who prayed using a pillow for rukoo’ and prostration “Pray on the ground if you can, and if you cannot, then tilt your head, and make your sujood lower than your rukoo’.” (Narrated by al-Bayhaqi with a strong (qawiy) isnaad, 4359. Classed as saheeh by al-Albaani in al-Saheeh, 323).
