Praise be to Allah.
Allah has commanded his slaves to establish prayer at the times that He has prescribed for it. He says (interpretation of the meaning):
“Verily, the prayer is enjoined on the believers at fixed hours”
He has made the timings of the prayer flexible for His slaves; He has appointed a beginning and end for them, and the time between the beginning, which is the best of its time, and the end, is sufficient time to pray. Whoever cannot pray at the beginning of the time has the option to pray until the end of that time comes. In the hadeeth of Jibreel (peace be upon him) it says that after the Prophet (blessings and peace of Allah be upon him) had offered the five obligatory prayers at the beginning of their times and the end, Jibreel said to him: “O Muhammad, these are the times of the Prophets who came before you and the time (for each prayer) is between these two times.”
Narrated by Abu Dawood, 332; classed as saheeh by al-Albaani (may Allah have mercy on him) in Saheeh wa Da‘eef Sunan Abi Dawood, 1/393
With regard to delaying the prayer until the time for it has ended, that is not permissible except in the case of one who has an excuse, such as if he fell asleep or forgot, because the Prophet (blessings and peace of Allah be upon him) said: “There is no negligence in (the case of) sleep; rather negligence is in the one who does not offer a prayer until the time for the next prayer comes.”
Narrated by Muslim, 1099
If a person is sick in that it is difficult for him to offer a prayer at the specified time, whether at the beginning or at the end, and he is also unable to offer the prayer standing or sitting or lying on his side, according to the report which confirms the concession granted to one who is sick, then he may put two prayers together, Zuhr and ‘Asr together, and Maghrib and ‘Isha’ together, putting them together either at the time of the earlier prayer or at the time of the later prayer, according to whatever is easy for him. And he should offer Fajr prayer at the proper time, until the reason that was preventing him from praying on time is no longer present.
Ibn Qudaamah (may Allah have mercy on him) said:
The kind of sickness that makes it permissible to put two prayers together is that which makes it too difficult to offer each prayer at its proper time because of hardship and weakness. Al-Athram said: it was said to Abu ‘Abdullah: Can the sick person put two prayers together? He said: I hope that he may do that if he feels too weak and is not able to do anything other than that.
End quote from al-Mughni, 2/59
And Allah knows best.