I am using this Tweet Archivist Desktop version, but I wonder if there is a way I can archive tweets that were posted 2 or 3 months ago?
No, it's not possible to archive tweets that were posted 2-3 months ago. According to the information found on the Documentation page, the software is capable of going back 3-4 week maximum.
To find more about it, access the documentation page: http://www.tweetarchivist.com/archivist-desktop/documentation.html