Let’s start with a basic understanding of the problem. From the perspective of the gemara, and even of the Rishonim, one may kasher between fleishig and milchig. (We will refer to milchig and fleishig interchangeably, as the direction of the switch makes no difference.) However, the Magen Avraham[1] reports a minhag not to do so. The rationale is that if one were allowed to kasher freely, he might decide to use a given utensil for both milchig and fleishig on an ongoing basis. Chazal were opposed to this situation, as the gemara[2] states that one should have three different knives to use for different functions and not rely upon himself to clean them well between uses. This minhag has been widely accepted and is considered binding in the Ashkenazic community.- Rav Ovadya Yosef[3] points out some weaknesses in the minhag and says that Sephardic poskim did not accept it.
Some important poskim understand that the prohibition does not really pertain to the use of a formerly milchig utensil for fleishig, but rather to kashering a utensil for that purpose. Consequently, if one kashered a utensil in order to prepare it for Pesach, he can change it from milchig to fleishig.[4] Similarly, if the utensil became treif and was subsequently kashered, it can be changed, as well.[5]
Rav Moshe Feinstein suggests that if no recognizable taste remains in the utensil (e.g., after kashering was already performed or after twelve months of nonuse), it might be permissible to change.[6] [7]Others permit kashering by a new owner, as he never used the utensil in a different manner and, thus, will not come to mistakenly use it for what it was originally (milchig or fleishig).[8] An interesting machloket exists regarding whether one can switch from milchig to pareve, given that even if he forgot to kasher the utensil before using it, the halachic stakes are much lower.[9] It is easier to be lenient when a pareve utensil accidentally becomes milchig because, without kashering, it can no longer be used for its original intended purpose.[10]
[The above is a brief survey of the topic and not a p’sak on any particular case.]