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Ammonium fumarate is the ammonium salt of fumaric acid. Salts generally have higher solubility in water compared to their corresponding acids due to the formation of ion-dipole interactions with water molecules. Therefore, ammonium fumarate is more soluble in water than fumaric acid.
Methanol is a polar solvent, but less polar than water. While both fumaric acid and ammonium fumarate exhibit some solubility in methanol, the solubility of both compounds is likely to be lower in methanol compared to water. This is because the strength of the interactions between the solute and methanol is weaker than those with water.