The technology that allows strands of DNA to be transferred from the cells of one species into another species is called genetic engineering or recombinant DNA technology.

Here's how it works:

1. Isolation of DNA: DNA is extracted from both the donor and recipient organisms.

2. Cutting DNA: Restriction enzymes are used to cut the DNA at specific sequences, creating fragments.

3. Ligation: The desired DNA fragment from the donor organism is then joined to the DNA of the recipient organism using an enzyme called DNA ligase.

4. Transformation: The recombinant DNA is introduced into the recipient organism. This can be done using various methods, such as using plasmids or viruses as vectors.

5. Selection and expression: Cells that have successfully incorporated the foreign DNA are selected and grown, allowing the expression of the desired gene.

This process allows for the transfer of genes across species, leading to the creation of genetically modified organisms (GMOs) with new traits.