The invention relates to the novel cotton variety designated 15R513B2XF. Provided by the invention are the seeds, plants, plant parts and derivatives of the cotton variety 15R513B2XF. Also provided by the invention are methods of using cotton variety 15R513B2XF and products derived therefrom. Still further provided by the invention are methods for producing cotton plants by crossing the cotton variety 15R513B2XF with itself or another cotton variety and plants and seeds produced by such methods.