The first thing you could try is to raise the needle (lower the clip) one notch and see if that takes care of the problem. Also, you might try richening up the fuel screw by turning it out a bit. However, if it is the flat-slide Delorto, it will have an air screw (located near the rear of the carb) instead of a fuel screw (located near front of the carb) which needs to be turned in instead of out to richen up the mixture. My '96 FE501 had the flat slide carb but the '97 and later bikes used the round slide carb along with '94 and earlier models (I believe the flat slide carbs were used for only a year or two). A friend I used to ride with years ago had a '92 FE350 and it had the round slide carb.
If the needle and/or the fuel screw doesn't fix the issue a richer pilot jet is in order and they are available (my Gas Gas trials bikes use the same pilot jets in their Delorto carbs as the older Husabergs). I don't know where you live but Rick at BOSS in Portland, OR has Delorto jets in stock and is only a phone call away, as are numerous other Husaberg, Gas Gas, Ducati, etc. dealers. The KTM LC4 models also used Delorto carbs, if I remember right.
Most likely you will be able to fix the issue by richening up the needle and/or the fuel/air screw.
