

TL;DR: No. The half-life of hydrogen-sulfide (one of smelliest constituents of a fart) reacting with the oxygen in the jar from just your fart is 12-37 hours. The article gives an example of a particularly potent hypothetical fart that would only retain any distinguishable odor for 9 days tops.
4% of a fart is oxygen, according to the article, which is enough to react with all of the hydrogen-sulfide, since 1 mole of oxygen is enough to react with more than 1 mole of hydrogen-sulfide (H₂S makes up around 1% of the total volume).