Keeping burgundy truffles is not very difficult, but, as all the fresh products, the best thing is to eat them quickly. With the fresh truffles is very interesting to put them in contact with the fat meals : eggs, fresh cream, butter, oil, etc…; after one or two days the truffles would have give all their flavor to the fat meals. To preserve the original taste, is not good to do a long cooking for the fresh truffles.
You can keep the fresh truffles maximum a week in a fridge, put the truffles in a box not really hermetique with a little peace of humid paper.
You can keep truffles 6 month in a freezer in an hermetique box, and you will use them just before the end of the decongelation, quickly, like fresh truffles .
You can keep them many years in Cognac and so, you will use for the long cooking of the meat. The Cognac is parfumed also with the taste of truffles, use it for the sauce or to flambe the meat.