Learn Spanish (Spain): Su madre es inglesa, por lo que habla inglés muy bien. - Her mother is English, which is why she speaks English very well.

por lo que translates to "which is why" or "so". While así que or por eso also work perfectly, por lo que is a relative connector that refers back to the entire previous situation (the fact that her mother is English). Using it elevates your sentence cohesion, which is expected in B2-level speaking and writing.

Why aren't the words inglesa and inglés capitalized?

Unlike in English, Spanish does not capitalize demonyms (words for nationalities like inglesa) or names of languages (inglés) unless they appear as the very first word of a sentence.

Why is there no definite article before inglés, such as habla el inglés?

While languages generally require the masculine definite article (el), there is an exception for certain verbs. You drop the article when the language immediately follows the verbs hablar, aprender, estudiar, saber, or entender, as well as after the prepositions en and de.

The translation assumes "Her mother", but since su is ambiguous, how would you clarify this if the context wasn't obvious?