This means:

See previous kudos below

Sociedad de Responsabilidad Limitada de Capital Variable. You can put that in ( ) afterwards, but leave the "S.A. de R.L. de C.V." as is because it is a specific corporate form under Mexican law.

Spanish term (edited): Capital social en una S de RL (LLC)

While it is true that "capital social" is often translated as "share capital" (UK) / "capital stock" (US), this is usually more appropriate for corporations (US) / public limited companies (UK) / sociedades anónimas, which issue interests known as "acciones" (shares/stock) that are negotiable.

In a Mexican S. de R.L. de C.V. these are known as "partes sociales" and are not negotiable.

From a UK/US perspective we'd still call them "shares", but clients sometimes insist on making the same distinction (between "acciones" and "partes sociales"/"participaciones" in Spain) in English.

So ideally, you'd want another term in English to avoid shares/stock, which could create confusion if your text makes reference to "acciones" further down the line.

Hence my suggestions "company capital", "equity capital", "owner's equity" to refer to the capital in a Mexican S. de R.L., which is divided not into "acciones" but "partes sociales". I think any of the three options would work.

For "partes sociales" you could use "equity interests", "member holdings" or even, more literally, "equity participations" or "participation units". The idea is to maintain a distinction from "acciones" (shares/stock), as required under Mexican/Spanish law.

Allow me to point you in the direction of several similar KudoZ questions; Rebecca Jowers gives several excellent explanations based on Spanish company law, which are well worth reading:
https://www.proz.com/kudoz/spanish-to-english/law-general/31...
https://www.proz.com/kudoz/spanish-to-english/finance-genera...
https://www.proz.com/kudoz/spanish-to-english/finance-genera...

These pages might also be useful:
https://difiere.com/diferencia-sa-de-cv-y-s-de-rl/
http://www.yucatancompass.com/articulo-lo-que-debes-saber/26...

This suggestion is for a US audience.

See the various options you get in the following Linguee search:
https://www.linguee.es/espanol-ingles/search?source=auto&que...

Some official sources avoid the use of the term "share capital" and instead use "holdings in the capital stock." I think the latter works well in this case.

The "non-negotiable stock limited liability corporation" part I found from a legal firm's website: http://www.lawmexico.com/wp-content/uploads/2016/01/Mexican-...

The "non-negotiable stock" part of the name refers to the fact that the stock cannot be transferred to any other party. This might be the more precise translation you are looking for in this case (again, for a US audience.)

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Note added at 6 hrs (2020-05-02 16:59:55 GMT)
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Sorry, my suggestion should rather read "Capital stock of a Mexican non-negotiable stock limited liability corporation."

Instead of shares, stockholders have holdings in the stock of the company. As EirTranslations suggested, you can leave the "S. de R.L. de C.V." and put in brackets next to it (Mexican non-negotiable stock limited liability corporation.) I just didn't have enough space to put that as an answer (it didn't allow me.)

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Note added at 9 days (2020-05-12 01:05:53 GMT) Post-grading
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Tienes razón. Creo que hay mucha confusión en el mundo de habla inglesa entre los significados de stock, capital y shares, lo que hace difícil a veces distinguir estos términos al traducir documentos de otros países.

Además de los aportes de Adrian y Joshua, también me he encontrado con las opciones de holdings y ownership interests, que tienen una asociación menos obvia con las acciones.