Officially no. California conservation camps, including Three Lakes Valley, are minimum security facilities where inmates work on fire suppression, conservation projects, and similar outdoor assignments. Internet access and social media are prohibited across all California Department of Corrections and Rehabilitation facilities regardless of security level. There is no authorized pathway for an inmate at any CDCR facility to access Facebook or send you a message through social media.
The unofficial picture is different, and conservation camps are actually more vulnerable to this than higher security facilities for a straightforward reason. Minimum security means reduced surveillance, more movement, more contact with the public during work assignments, and less rigorous screening than you would find at a higher custody facility. The combination of those factors makes it easier for smartphones to find their way in, whether through a sympathetic guard, a visitor, or contact made during an outside work detail.
If you are receiving Facebook messages or seeing social media activity from someone at Three Lakes Valley, it is almost certainly coming through a contraband phone. That is a serious infraction that carries significant consequences if discovered, including removal from the camp program, loss of the privilege of minimum security placement, and potentially new criminal charges under the law that made possession of a cell phone by an inmate a federal crime.
If your person is reaching out through Facebook and you care about their situation, the most helpful thing you can do is encourage them to use legitimate communication channels instead. The risk of losing camp placement over a social media message is not worth it when letters, phone calls, and email through CorrLinks are all available.