The thing to remember is that in normal sexual reproduction, the father has two sets of chromosomes, and crossing over takes place between the chromatids of each pair during the meiosis which produces the sperm. Therefore, "the sperms are not identical", because in each chromosome of a pair there will be different alleles at many of the loci. But when the father is haploid "all the sperm will be identical" (except for a small number where gene mutations have taken place in the germline). So, "as long as all the female queen mates only with one male", all the female offspring will inherit the male's chromosome 100% intact. In fact in Hymenoptera, the males almost all produce enough sperm to last the female for a whole lifetime.