Manturov's parity group projection conjecture for connected sums

Let $K_1$ and $K_2$ be representatives of virtual knots $[K_1]$ and $[K_2]$, and choose any connected sum $K_1\#K_2$. Let $upr$ denote Manturov's parity group projection from virtual isotopy classes of knots to isotopy classes of classical knots. Manturov's conjecture. For any such representatives and any choice of connected sum, there is an equality

$$upr(K_1\# K_2)=upr(K_1)\# upr(K_2).$$

The conjecture asserts that the parity group projection is compatible with connected sum, despite the fact that the connected sum of virtual knots is not generally well-defined independently of representatives and the chosen cylinders. Its status is not established in the supplied source.