The conversion requires a new barrel (you had probably guessed) and possibly a new slide so the case head fits the breech and the extractor engages properly.
The two rounds are very close dimensionally (one of the reasons just about everyone who makes a 9x19 pistol also makes a .40 S&W) and the 9x19 extractor and breech face might fit without alteration. Or might not. The same for the magazines; but alternative magazines are available.
The only problem is IF the conversion would be cheaper than simply buying another pistol.