  Let R be a local domain, v a valuation of its quotient field centred in R at
its maximal ideal. We investigate the relationship between R^h, the
henselisation of R as local ring, and {\~v}, the henselisation of the valuation
v, by focussing on the recent result by de Felipe and Teissier referred to in
the title. We give a new proof that simplifies the original one by using purely
algebraic arguments. This proof is moreover constructive in the sense of Bishop
and previous work of the authors, and allows us to obtain as a by-product a
(slight) generalisation of the theorem by de Felipe and Teissier.
