"The jacket is his."
Translation:La chaqueta es suya.
My original answer was as you posted but it said I was wrong and gave me this? El chaquetón es suyo.
Me too then I noticed I'd got el chaqueta, not la, which explained all. Damn autocorrect (any excuse eh?)
So basically the owner of the jacket is unknown in this sentence. It could be his, hers, or theirs.
Because it is his jacket I think the answer should be suyo instead of suya. Por ejemplo: La chaqueta es suyo.
The possessive suya is following the gender of the noun 'chaqueta' which is feminine.
The short form possessives - mi, mis, tu, tus, su, sus don't follow gender but the long form possessives do:
mio, mia, mios mias - mine, my
tuyo, tuya, tuyos, tuyas - your, yours (familiar, tú)
suyo, suya, suyos, suyas, his, hers, their, theirs your, yours (formal, usted)
nuestro, nuestra, nuestros, nuestras, our, ours
vuestro, vuestra, vuestros, vuestras - your, yours, (familiar plural)
The possessives don't reflect the gender of the owner. They always agree with the thing that is possessed.
That's why "La casA es suyA" can mean, among other things, "The house is theirs" even if we're talking about a father and his two sons.