Whether the behavioural special relativity principle implies the body–observer special relativity principle

Let ${{\mathsf{SPR}}}\xspace^+$ denote the behavioural formulation of the special principle of relativity, and let ${{\mathsf{SPR}_{{{\mathit{B}}}\xspace}}}\xspace$ denote the body-based formulation. Open problem. It is unclear whether

$${{\mathsf{SPR}}}\xspace^+ \Longrightarrow {{\mathsf{SPR}_{{{\mathit{B}}}\xspace}}}\xspace.$$

The paper states that this question remains open because it is unclear whether ${{\mathsf{SPR}}}\xspace^+$ is sufficient, on its own, to entail ${{\mathsf{SPR}_{{{\mathit{B}}}\xspace}}}\xspace$.