Hfr strain differs from F+ strain because
F+ strains carry autonomous F plasmid extrachromosomally, expressing pili and transferring only F DNA in crosses, donor ability but chromosomal genes transfer at very low frequency. Hfr strains arise when F integrates into bacterial chromosome via homologous recombination at IS elements, creating single linkage between F origin oriT and chromosome. Upon conjugation, transfer initiates at integrated oriT and proceeds linearly into chromosomal DNA, transferring chromosomal markers with high efficiency in order determined by integration site and orientation, converting recipients to recombinants for those alleles while remaining F- unless whole chromosome transfers.
Ref: Wollman & Jacob 1956, Comptes Rendus; Griffiths et al., Chapter 6: Hfr vs F+ Biology