Quotients of zero-dimensional precompact abelian groups

Shakhmatov (1990) proved that precompact groups can be presented as quotients of zerodimensional precompact ones with preservation of the weight. We obtain here a new proof of this result in the abelian case making no use of free topological groups. We study the question when various properties (total minimality, being torsion-free, etc.) can be preserved under this process of lifting.