If the trp1 and trp2 mutations map close to each other, one would cross strains A and B and select exconjugants that are cys+ and resistant to the phage Z. If trp1 and trp2 are alleles of the same locus, then a cross between strains A and B will not result in trp+ cells; if they are not allelic, strain B cells that have received the F′ from strain A will be trp+ (complementation). Strain C is not useful for this experiment.
If the genes are not close, then a second approach would be to try transforming B with C; select cys+ and see if trp+ recombinants are ever seen even at high plating densities.