Is it permissible to record religious programs broadcast on satellite channels, such as "The True Promise" and "Following in the Footsteps of the Beloved," in order to benefit from them and keep them as a reference in a home library?

There is no objection to recording the materials and keeping them in a private library for personal benefit. Indeed, this is the aim of those who produce the programs. What is forbidden is recording these programs and trading them without the owner's permission.