Is there a finitely generated residually finite group with solvable word problem that does not embed in a finitely presented residually finite group?

In paragraph 1.1.7 of of a recent preprint of Kharlampovich--Myasnikov--Sapir, the authors write:

We expect the approach used in this paper to be useful in solving other problems that are still open. For example, the residually finite version of the Higman embedding theorem would be very desirable.

In particular, the problem seems to be open.

I'm not sure how the approach of that paper might apply to the problem at hand.

A preprint by E. Rauzy appeared today on the arXiv, and gives a negative answer to this question. In other words (if the proof is correct), there exists a f.g. residually finite group with decidable word problem which does not embed in a f.p. residually finite group.