I think "его" means "his" mom, but for other "he". If you want to mean that this "he" is the same as the first, then you should use "свою".
I'm making up stuff from what I know, because I find this similar to Esperanto (sia/lia), I'm not sure though.
Li amas lia patrino -> "He loves his mother", but the 2nd "he" is not the same person as the 1st one.
Li sxatas sia patrino -> "He loves his mother", the 2nd "he" is the same person as the 1st one.
This pronoun свой strikes me as having a curious likeness in both form and meaning to Latin suus/sua/suum. Is it possible that the Latin pronoun somehow filled a blank in Byzantine Greek, found acceptance in that language, and was transmitted to Russia along with many other fragments of Greek culture when the Russians adopted a largely Greek form of Christianity? Or is this (as seems more likely to me) something that goes back almost to the roots of Indo-European and has survived in parallel, rather than as a derivative, in both Latin and the Slavonic languages? There is a very similar phenomenon in the verb внднт, '[he/she] sees', which is almost the same as its Latin equivalent; that is properly videt but is often found written vidit in late antiquity.
I majored in linguitics at university, and while I'm not up on my Indo-European, I suspect you're right in the latter case rather than the former: that it was a feature of Indo-European that has survived in its different descendant languages in different forms snd ways. After all, English has the word "myself," or rather, the particle "-self," too; it just has to agree in inflection with its subject: myself, yourself, herself, himself, itself, themselves, etc. In this case, Russian is actually simpler, or perhaps it's better to say more efficient, in that it has preserved it as a single word, while English (and many other languages) require it to be highly inflected. It's the complexity of the English form that makes it difficult to recognize the same, but in simpler form, in Russian.
To my knowledge, both "Он любит свою маму" and "Он любит его маму" would both translate to "He loves his mom"; however, they have different meanings and are not interchangeable. Using "свою маму" means that the man loves his own mom, whereas "его маму" would indicate that he loves another man's mom.
A quick look on Wiktionary tells me that него́ is an alternative form of the pronoun его́, and него́ is used when the pronoun comes after a preposition.
However, in the case of our sentence, его́ is acting as a possessive adjective, so grammatically него́ is not applicable here at all.
It's like the difference in English between "I know her" and "That is her dog".
From the comments here it seems like it's similar in principle to Norwegian:
Han elsker moren sin - he loves his mom -- он любит свою маму
Han elsker moren hans - he loves his mom -- он любит его маму
Both mean his in English but the first is a man who loves his own mom, the second is a guy who loves some other guys mom.
Have I understood the difference correctly?