The Prophet sallahu alayhi wa salam said:
إذا أفطر قال ذهب الظمأ وابتلت العروق وثبت الأجر إن شاء الله
He (Ibn Umar) said that the Prophet (ﷺ) said when he broke his fast: Thirst has gone, the arteries are moist, and the reward is sure, if Allah wills.
[Saheeh Sunan Abi Dawood no. 2357]
Imam al-Adheemabaadi rahimahullah said:
إذا أفطر ) أي بعد الإفطار
When he broke his fast: that is: after breaking the fast
Shaikh Salih al-Fawzan hafidhuhallah mentions that it should be read in summer and winter here
Shaikh Abdul-Muhsin al-‘Abbad hafidhuhallah was also asked:
The dua “The Thirst has gone, the arteries are moist…” and “Oh Allah I fasted for you, I believe in you, and with your provision I break my fast”.
When are they said: after breaking the fast or when breaking the fast?
When breaking the fast. When you break your fast, you mention it. The authentic Hadith is the first one. As for the second one, it is not established
[Sharh Saheeh al-Bukhari no. 181 side B]
The second dua the Shaikh is referring to is the famous one most people use, but is not authentic:
اللهم لك صمت وبك آمنت وعلى رزقك أفطرت
So it seems that a person can say this dua before or after breaking the fast.
And Allah knows best
Faisal Ibn Abdul Qaadir Ibn Hassan