Officially, no. Inmates at Leath Correctional Institution in South Carolina, like inmates at virtually every correctional facility in the country, are not permitted to access the internet or social media platforms. Facebook accounts, Instagram, and similar platforms are explicitly prohibited, and maintaining an active social media presence while incarcerated violates both facility rules and in some cases the terms of service of the platforms themselves.
The unofficial reality is more complicated. Smartphones are smuggled into facilities every day across the country, and Leath is not an exception to that pattern. The supply chain for contraband phones inside correctional facilities is well-documented and includes staff members as transporters, which is part of why the problem persists despite ongoing efforts to stop it. Metal detectors do not catch phones hidden in creative ways, and the financial incentive to bring one in is significant enough that the risk calculus works for some people.
If you are seeing posts or activity on a social media account that appears to be coming from someone inside, there are a few possibilities. They have access to a contraband phone and are posting directly. Or they are using a third-party service, which does exist, where someone on the outside manages and posts content on behalf of an inmate for a fee, relaying messages and updates through phone calls or letters.
Whether this information is relevant to your specific situation depends on what prompted the question. If you are concerned about someone inside managing communications in ways that affect you, that concern is worth trusting.