We study the $I$-$V$ characteristics of S$_{\text{T}}$/n/N contacts, where S$_{\text{T}}$ is a BCS superconductor S with a built-in exchange field $h$, n represents a normal metal wire, and N---a normal metal reservoir. The superconductor S$_{\text{T}}$ is separated from the n-wire by a spin filter which allows the passage of electrons with a certain spin direction so that only fully polarized triplet Cooper pairs penetrate into the n-wire. We show that both the subgap conductance $\sigma_{\text{sg}}$ and the excess current $I_{\text{exc}}$, which occur in conventional S/n/N contacts due to Andreev reflection (AR), exist also in the considered system. In our case, they are caused by unconventional AR that is not accompanied by spin flip. The excess current $I_{\text{exc}}$ exists only if $h$ exceeds a certain magnitude $h_{\text{c}}$. At ${h < h_{\text{c}}}$ the excess current is converted into a deficit current $I_\text{{def}}$. The dependencies of the differential conductance and the current $I_{\text{exc}}$ are presented as a function of voltage and $h$.