✅Answer: No narration has been reported to answer this question, and this is one of the matters that only the Proof of Allah can clarify. To hasten the finding of the answer to this and similar questions, we all say with humility and in abundance:

اللَّهُمَّ صَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ

وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ

✅However, in a hadith from our Master, Imam al-Mahdi, peace and blessings of Allah be upon him, he refers to a hadith in his answer to a question about fasting in the month of Rajab. Since the full text of the hadith requires its own specific explanation, we will mention the full text of the hadith and only translate the relevant part:

1 أَحْمَدُ بْنُ عَلِيِّ بْنِ أَبِي طَالِبٍ الطَّبْرِسِيُّ فِي الْإِحْتِجَاجِ عَنْ مُحَمَّدِ بْنِ عَبْدِ اللَّهِ بْنِ جَعْفَرٍ الْحِمْيَرِيِّ عَنْ صَاحِبِ الزَّمَانِ صلوات الله علیه أَنَّهُ كَتَبَ إِلَيْهِ أَنَّ قِبَلَنَا مَشَايِخَ وَ عَجَائِزَ يَصُومُونَ رَجَباً- مُنْذُ ثَلَاثِينَ سَنَةً وَ أَكْثَرَ وَ يَصِلُونَ شَعْبَانَ بِشَهْرِ رَمَضَانَ- وَ رَوَى لَهُمْ بَعْضُ أَصْحَابِنَا أَنَّ صَوْمَهُ مَعْصِيَةٌ فَأَجَابَ قَالَ الْفَقِيهُ يَصُومُ مِنْهُ أَيَّاماً إِلَى خَمْسَةَ عَشَرَ يَوْماً ثُمَّ يَقْطَعُهُ إِلَّا أَنْ يَصُومَهُ عَنِ الثَّلَاثَةِ الْأَيَّامِ الْفَائِتَةِ لِلْحَدِيثِ إِنَّ نِعْمَ شَهْرُ الْقَضَاءِ رَجَبٌ.

📚 Al-Ihtijaj, p. 488.

Our Master, Imam al-Mahdi, peace be upon him, at the end of the above narration, refers to a hadith, the translation of which is:

'Indeed, Rajab is a good month for making up missed fasts.'

✅From the above narration, the special virtue of the month of Rajab for making up missed fasts is inferred.

✅For a more detailed explanation, refer to the people of knowledge, and you will soon receive the most complete possible answer, God willing, from the presence of the Remainder of Allah, peace and blessings of Allah be upon him. To reach such a day quickly, let us say:

اللَّهُمَّ أَرِنِی الطَّلْعَةَ الرَّشِیدَةَ وَ الْغُرَّةَ الْحَمِیدَةَ وَ اکْحُلْ نَاظِرِی بِنَظْرَةٍ مِنِّی إِلَیْهِ وَ عَجِّلْ فَرَجَهُ وَ سَهِّلْ مَخْرَجَهُ وَ أَوْسِعْ مَنْهَجَهُ وَ اسْلُکْ بِی مَحَجَّتَهُ