All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

It is incumbent upon a Muslim to maintain performing prayers on their prescribed times as much as possible. The proof of this is that Allah the Almighty says {What means}: " For such prayers are enjoined on believers at stated times." {An-Nisa`, 103}. Moreover, Narrated Al-Walid bin 'Aizar:

I heard Abi `Amr 'Ash-Shaibani saying, "The owner of this house." he pointed to `Abdullah's house, "said, 'I asked the Prophet (PBUH) 'Which deed is loved most by Allah?" He replied, 'To offer prayers at their early (very first) stated times.' {Transmitted by Bukhari}.

If the doctor is able to delay the surgery or perform the prayer before it or after it, but there is sufficient time to offer it within its prescribed time, then delaying the prayer is prohibited.

If it becomes difficult to do so, the scholars, may Allah have mercy on them, have permitted advancing or delaying the prayer due to necessity, or if there is fear that performing it on time would result in missing a religious obligation or missing a benefit that the Sharia encourages to preserve, such as protecting life, wealth, or honor. 

 In his commentary on {Asnā al-Maṭālib, Vol.1/Page 274}, Al-Ramli, may Allah have mercy on him, said: "His saying about delaying [the prayer] for combining, this is applicable as Sadr al-Din al-Jazari mentioned in dealing with saving a drowning person, repelling harm from oneself or property, and praying for a deceased person when there is a fear of their body exploding."

In {Baghiyat al-Mustarshidin fi Takhrij Fatawa Ba‘d al-A’imma min al-Mutaakhireen, Vol.2/Page 275}, it is mentioned: "Al-Khattabi narrated from Abu Ishaq its permissibility for the resident (Non-traveler) due to necessity, even if there is no fear, rain, or illness, and Ibn al-Mundhir supported this view."

It is stated in {Al-Insaf fi Ma'rifat al-Rajih min al-Khilaf, Vol. 2/Page 336}, one of the books of the Hanbali scholars,: "Combining prayers is permissible for someone who has occupation or a valid excuse that permits missing the Friday and congregational prayers, such as fearing for oneself or honor, financial constraints, or other similar reasons."

In conclusion, if the doctor is occupied with performing a surgical operation, and it becomes difficult for him to perform the prayer at its designated time due to concern for the patient`s life, it is permissible for him to intend to combine the prayers later. And Allah the Almighty knows best.