Shaykh Abd-Allaah ibn Qaood answered this question for us as follows:
We do not know of any evidence to that effect. Allaah may answer the duaa of one who calls on Him in desperation even if he is a kaafir. And Allaah knows best.
Does not praying at the beginning of the appointed time mean that one’s du’aa’ will not be answered?
Question: 3935
Is there any evidence that one who delays prayer from its recommended time (but prays in its legal time) and who makes post-salah
du'ah does not have his/her du'ah accepted?
Answer
Praise be to Allah, and blessings and peace be upon the Messenger of Allah.
Source:
Islam Q&A - Sheikh Muhammed Salih Al-Munajjid
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