No problem as long as he didnt eat anything after Fajr. However, his reward won’t be full as someone who made his intention before Fajr.

sheik, if a person performs voluntary fasts of monday & thursdays after fajr , i mean he makes his intention after 10 am & completes after maghrib, is it permissible ? will this person gets the reward of fasting?

Fasting | April 23, 2017 4:01 am
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Some of my relatives say that a nawafil fast will not be valid if we skipped any sunnah prayer of the day we were fasting. Is it correct? And is it okay to do Sajda once in a while after fardh salah, just like that, thanking Allah for everything?
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My father is 70 years old and is on medication. This medication can be taken outside fasting hours however at his age he beginning to find the fasting, especially the long hours in the UK difficult as he experiences from a lot of thirst immediately after suhoor. He has fasted all his life but is asking if it permissible to give fidyah this year? Is this allowed for him?