How to encode a partial MaxSAT problem to PBO(Pseudo Boolean Optimization)

Example. Consider the following weighted partial MaxSAT instance.
\phi_h = { (x1 ∨ x 2 ∨ ~x3 ),(~x2 ∨ x3 ),(~x1 ∨ x3 )}
\phi_s = { (~x3 ,6),(x1 ∨ x2 ,3),(x1 ∨ x3 ,2)}
(2)
According to the described encoding, the corresponding PBO instance would be:
minimize 6s1 + 3s2 + 2s3
subject to x1 + x2 + ~x3 >= 1
~x 2 + x3 >= 1
~x 1 + x3 >= 1
s1 + ~x3 >= 1
s2 + x1 + x2 >= 1
s3 + x1 + x3 >= 1

Algorithms for Weighted Boolean Optimization, by Vasco Manquinho, Joao Marques-Silva, Jordi Plane