If one has fast to make up why not make them up in this blessed month.
Making up Missed Fast-Days
Someone obliged to make up some fast-days of Ramadan is recommended to do so consecutively and immediately.
it is not permissible for a person with some unperformed fast-days of Ramadan to delay making them up until next Ramadan unless there is an excuse(for delaying). If one delays until the next Ramadan, one must pay 0.51 liters of food (to the poor) missed, in addition to making it up. If making up a fast-day is delayed until a second Ramadan comes, then one must pay a double this amount for each day. And so forth: every year that passes upon an unfilled fast-day adds 0.51 liters to be paid for that day. (But if one’s excuse for not performing them persist, such as travel or illness then it is permissible for one to delay making them up as long as the excuse is present, even if it lasts for years. One is not obligated to pay the penalty fee for this delay even if several Ramadans go by, but is merely obliged to make up the missed fast-days)
Taken from Reliance of the Traveller pg 290-291
A HADITH ON FASTING IN RAJAB
Imam al-Nawawi said:
“Neither prohibition nor praiseworthiness has been established for the month of Rajab in itself, HOWEVER,
(1) the principle concerning fasting is that it is praiseworthy in itself, and
(2) in the Sunan of Abu Dawud the Prophet has made the fasting of the sacred months praiseworthy, and Rajab is one of them.”
A Hadith On Fasting in Rajab
1. `Uthman ibn Hakim al-Ansari said: “I asked Sa`eed ibn Jubayr about fasting in Rajab, and we were then passing through the month of Rajab, whereupon he said: “I heard Ibn `Abbas saying: “The Messenger of Allah used to observe fast so continuously that we thought he would not break it, and did not observe it so continuously that we thought he would not observe fast.” Muslim and Abu Dawud relate it in Kitab al-sawm, respectively in the chapter on fasting at times other than Ramadan, and in the chapter of fasting during Rajab.
Imam Nawawi says: “It would appear that the meaning inferred by Sa`eed ibn Jubayr from Ibn `Abbas’s report is that fasting in Rajab is is neither forbidden nor considered praiseworthy in itself, rather, the ruling concerning it is the same as the rest of the months. Neither prohibition not praiseworthiness has been established for the month of Rajab in itself, however, the principle concerning fasting is that it is praiseworthy in itself, and in the Sunan of Abu Dawud(*) the Prophet has made the fasting of the sacred months praiseworthy, and Rajab is one of them. And Allah knows best.” Sharh Sahih Muslim Kitab 13 Bab 34 #179.