  We study the Josephson effect in a trijunction formed by two topological
superconductor (TS) wires and a conventional $s$-wave superconductor. Using a
boundary Green's function formalism, analytical results for the current-phase
relation are obtained in various limiting cases by modeling the TS wires via
the low-energy limit of a Kitaev chain. We show that Josephson transport
critically depends on the spin canting angle $\theta$ between the boundary spin
polarizations of the TS wires, which in turn suggests that the spin structure
of Majorana states can be accessed through supercurrent measurements. We also
extend the boundary Green's function approach to a more microscopic spinful
wire model and thereby compute the dependence of $\theta$ on experimentally
accessible parameters such as the Zeeman field and/or the chemical potential.
Furthermore, we show that the equilibrium current-phase relation between both
TS wires exhibits a robust $4\pi$-periodicity since the conventional
superconducting lead effectively locks the fermion parity of the trijunction.
