The monetary expansion puts downward pressure on the exchange rate. To prevent it from falling, the central bank starts buying domestic currency in greater quantities to “prop up” the value of the currency in foreign exchange markets. This buying removes domestic currency from circulation, causing the money supply to fall, which shifts the LM* curve back.
Another way of looking at it: To keep the exchange rate fixed, the central bank must use monetary policy to shift LM* as required so that the intersection of LM* and IS* always occurs at the desired exchange rate. Unless the IS* curve shifts right (an experiment we are not considering now), the central bank simply cannot increase the money supply.