Is expiation obligatory for one who intentionally ejaculates while fasting, and what is Malik's view on this, and is it permissible to authorize someone in another country to give the food (as expiation) if the answer is yes?

For one who experiences a seminal emission due to contemplation, their fast is not invalidated according to the Hanafis, Shafi'is, and Hanbalis. They cite the hadith (definition): "Indeed, Allah has pardoned for my Ummah that which they whisper to themselves or that which their souls incline to, as long as they do not act upon it or speak of it."

As for the Malikis, if one experiences a seminal emission due to prolonged contemplation, and it is their habit to experience emission when they contemplate, their fast is invalidated, and they must make up the fast (qada') and offer expiation (kaffara). If the contemplation was not prolonged, then they only need to make up the fast. However, if it went beyond what is customary, then the make-up fast is waived. The expiation is to free a slave; if that is not possible, then to fast for two consecutive months; if unable to do that, then to feed sixty poor people. It is permissible to appoint someone else to give out the expiation in another country if the people there are in greater need.

A fasting person must avert their thoughts from anything that incites desire.