A bacterial cell that possesses the F factor integrated into the bacterial genome, hence, when it conjugates with another bacterium, it attempts to transfer a copy of the F factor as well as a portion of or the entire chromosome to the recipient bacterium.
Hfr stands for high frequency of recombination first described by the population geneticist, Luca Cavalli-Sforza. The bacterial cell that acquires F plasmid and incorporates to the bacterial chromosome through crossover, the cell is now designated as Hfr.
During conjugation, the Hfr bacterium would attempt to transfer its entire DNA to the F-bacterium. However, since the mating bridge is structurally fragile the genetic transfer is often incomplete. Hence, the recipient bacterium may only receive a portion of, and rarely the entire, bacterial genome of the donor Hfr bacterium.