Rational points transfer from residue fields to henselian defectless fields

Let $K$ be a henselian defectless valued field with divisible value group and residue field $k$. A field has the separably rationally connected rational-point property if every separably rationally connected variety over it has a rational point. Rational-point transfer conjecture. If every separably rationally connected $k$-variety has a $k$-point, then every separably rationally connected $K$-variety has a $K$-point. The statement appears in a section titled “Goal” and is marked “In progress” in the source; no proof or resolution is supplied in the provided text.