Imām Muḥammad ibn Ṣāliḥ al-ʿUthaymīn [d. 1421 AH] said:
The example of the person of which fasting becomes obligatory in the middle of the day—such that this person is subjected to either fasting [immediately] or on another day—[includes]:

1. the woman whose menses cease,
2. a woman whose postpartum period finishes,
3. and a traveller who returns home [during the day] whilst not in a fasting state.
4. These are three issues to which we will add a fourth: a sick person who makes a recovery.

   We collectively liken this to the issue of removing that which prevents the fast during the day [of obligatory fasting]. So, in such cases would it be compulsory to begin fasting immediately, then fast another separate day in its entirety?

We reply: As for fasting a separate day, there can be no doubt regarding its compulsory nature. This is because they have intentionally broken their fast during one of the days of Ramaḍān [with a valid reason] and as such they must fast another day to compensate for this one as Allāh says:

وَمَن كَانَ مَرِيضًا أَوْ عَلَىٰ سَفَرٍ فَعِدَّةٌ مِّنْ أَيَّامٍ أُخَرَ ۗ ‎﴿١٨٥﴾‏

‘And whoever is ill or on a journey – then an equal number of other days.’
[Al-Baqarah, 2:185]

And for the saying of ʿĀʾishah (may Allāh be pleased with her): ‘We used to be ordered with fulfilment [of the missed days of] fasting, but we were not ordered with fulfilment of [missed] prayers’, she meant by this the menstruating women.

As for [these individuals] starting their fast immediately during the middle of the day, it is the opinion of the [Ḥanbalī] madh`hab that it is obligatory. This is because they have only broken their fast as a consequence of a preventive factor that has now abated, and a ruling should be suspended whenever its causative rationalisation is absolved. There is another narration from Imām Aḥmad [ibn Ḥanbal] that fasting immediately is not obligatory because it is perfectly apparent and implicitly permissible for them to leave fasting at the start of the day in question and engage in eating, drinking, and other activities that would break the fast. As such, they do not derive any kind of benefit from restraining themselves spontaneously from these things arbitrarily in the middle of the day. Moreover, the sanctity of the day itself has already been nullified by their lawful abandonment of the fast at the start of the day.

It was narrated from Ibn Masʿūd (may Allāh be pleased with him):

‘Whomsoever eats at the start of the day, let him eat at its end.’ which means that whomsoever has permission to [break his fast] through eating at the start of the day will have that permissibility extended to the day’s end.

Source: Al-Sharḥ al-Mumtiʿ 6:335
Translated by: Riyāḍ al-Kanadī