The formation of a new nuclear membrane around the chromosomes occurs during the telophase stage of mitosis.
During telophase, the separated chromatids reach the poles of the cell. As the cell prepares to divide, the chromosomes begin to de-condense back into their less tightly coiled state. This is when the nuclear envelope reforms around each set of chromosomes, creating two distinct nuclei in the two daughter cells. This event is crucial for ensuring that each daughter cell receives its own complete set of genetic material, maintaining the integrity of the cellular function.