There are numerous narrations that show the time after the prayer is one in which du’a is answered. Abu Umamah al-Bahili asked the Prophet, peace be upon him, ‘O Messenger of Allah! Which du’a is the most likely to be responded to?” He, peace be upon him, replied:
“In the last part of the night, and after the obligatory prayers.” (Recorded in al-Tirmidhi)
In fact, the Prophet, peace be upon him, stressed this time period to those whom he loved, for he said to Muadh ibn Jabal:
“O Muadh! I swear by Allah, I love you. Therefore, do not forget to say after each prayer, ‘O Allah help me to remember You, and to thank You, and to perfect my worship of You.” (Recorded in Abu Dawud)
It should be noted that there is a difference of opinion amongst the scholars over the exact meaning of ‘…after the obligatory prayers,’ and this stems from the Arabic word that is used to convey the meaning of the word ‘after’, which is dubur. Some scholars such as Ibn Taymiyyah, considered the meaning of this hadith to apply to the time before one says the final salam of the prayer, and after one has finished reciting tashahhud. So, according to those that follow his opinion, the word dubur would translate as ‘at the end’, and not, ‘after’. According to this opinion the time period would be the same as that mentioned in the previous post, about du’a before the end of salah.
However, other scholars understand this hadith to mean the time period after the prayer finishes, and the word carries both meanings as Ibn al-Qayyim has mentioned.