Palm construction conjecture for critical Hawkes processes

Let $F$ be a displacement distribution and let $N_0$ be the random counting measure constructed from the renewal and random-walk occupation measures in the paper, with distribution $L_0$. Let $\lambda>0$. Palm construction conjecture. If $F$ is transient, then $N_0$ defines a point process, and $\lambda L_0$ is the Palm measure of a stationary point process with finite average intensity $\lambda$, namely the critical $(\lambda,F)$-Hawkes process. The construction connects transience to local finiteness and to the existence of a stationary critical Hawkes process; the supplied text gives no resolution of the assertion.