Observing Sawm on Mondays and Thursdays is not only restricted to Rajab or Sha'ban, rather it is a Mandub (commendable) act during all the months of the year. It is also permissible for whoever is in the habit of fasting them all year to observe fasting them after the fifteenth of Shażban, even if one of these days coincides with the Day of Doubt (so called because there is doubt concerning it - is it the last day of Sha'ban or the first day of Ramadan), for the Prophet (peace be upon him) said: Do not observe fast for a day or two days ahead of Ramadan, except a person who is in the habit of observing a particular Sawm; they may fast on that day. (Agreed upon its authenticity by Al-Bukhari and Muslim)
May Allah grant us success! May peace and blessings be upon our Prophet Muhammad, his family, and Companions!