Learn Spanish (Latin America): El paraguas negro es el suyo.

The pronoun el suyo can mean his, hers, yours (formal), or theirs. You usually know which one it is from the context of the conversation. In this standalone sentence, the English translation is what tells us it means "his".

If the umbrella belongs to a woman (hers), does it change to "la suya"?

No, it stays as el suyo. Possessive pronouns in Spanish always match the gender and number of the thing being owned, not the owner. Since el paraguas is masculine and singular, the pronoun replacing it must be el suyo, no matter who owns it.

Why does "paraguas" end in an "s" if we are only talking about one umbrella?

Paraguas is a compound word made of para (stops) and aguas (waters). These types of words naturally end in an "s" but are masculine singular when talking about one item. If you wanted to talk about multiple umbrellas, the noun wouldn't change, but the article would become plural: los paraguas.

Can I leave out the "el" and just say "es suyo"?

Yes, you can! When a possessive pronoun comes right after the verb ser (like es in this sentence), you can often drop the article. Saying es suyo is very common and sounds natural. Keeping el suyo is also correct and puts a little more emphasis on it being "his one" compared to the other umbrellas.