Final answer:
The term for the conversion from Hfr to F' that carries bacterial genes is a process involving the imprecise excision of the F plasmid, which can transfer part of the bacterial chromosome to an F- recipient during conjugation.
Step-by-step explanation:
The conversion from Hfr to F' which carries bacterial genes along with it is a process that occurs during bacterial conjugation. When an Hfr cell with the integrated F plasmid attempts to transfer its DNA to an F- cell, the entire chromosome starts to transfer. However, because conjugation may end prematurely, not all chromosomal DNA is transferred. If the F plasmid is excised imprecisely from the chromosome, the F' plasmid will carry with it chromosomal genetic material. This F' plasmid can then be transferred to an F- cell, introducing new genetic material to the recipient bacterium. This process is instrumental in mapping out the bacterial genome and can lead to new genetic combinations, aiding bacterial adaptation and evolution.