When a foreign DNA is introduced into an organism, how is it maintained in the host and how is it transferred to the progeny of the organism?

Explanation

Foreign gene is usually ligated to a plasmid vector and introduced in the host. As plasmid replicates, and makes multiple copies of itself, so does the foreign gene gets replicated and its several copies are made. When the host organism divides. Its progeny also receives the plasmid. DNA containing the foreign gene.
The whole process can be visulaised in the figure given b elow.