The earliest discovered molecular form of the elemental phosphorus is white phosphorus $(\ce{P_\mathrm{W}})$, which was isolated in 1669 by a German alchemist, Hennig Brand (Ref.1). Later in 1914, Percy Bridgman has introduced the phase transition of white phosphorus to black phosphorus $(\ce{P_\mathrm{B}})$ under high pressure (Ref.2). The irreversible transformation was observed when white phosphorus was left at $\pu{200 ^\circ C}$ under $\pu{12000 kg cm-2}$ $(\approx \pu{12000 bar})$ pressure for about $\pu{15 min}$. Ref.2 remarks the observation as follows:
On taking the apparatus apart the next morning it was found that the phosphorus had been transformed indeed, but not to the familiar red form, but to another modification that is apparently quite new. The new form is grayish black like graphite, breaks with a similar greasy looking fracture, and will mark on paper. It is stable in the air although slightly deliquescent, is ignited with difficulty by a match, and cannot be exploded by a blow from a hammer, as red phosphorus can. It is a conductor of electricity and a rectifier. The most definite characteristic is its high density, 2.69 against 2.34 for the red variety, and I.9 for the yellow. The experiment was repeated twice, successfully each time. Once it was necessary to go to nearly I3,ooo kgm. to start the transformation. The time necessary to force the reaction to start may also vary considerably. An attempt to similarly transform the commercial powdered red phosphorus into the new variety by subjecting it to 200o and I3,ooo kgm. for over half an hour was without result.
According to this excerpt, it is pretty sure that Bridgman has produced the first batch of $\beta$-$\ce{P_\mathrm{B}}$, which conduct electricity:
This excerpt is also proved that the way of how to make black phosphorus reported in Lumen Learning:
Black phosphorus is obtained by heating white phosphorus under high pressures (about 12,000 standard atmospheres, or 1.2 gigapascals). In appearance, properties, and structure, black phosphorus resembles graphite — it is black and flaky, a conductor of electricity, and has puckered sheets of linked atoms.
Accordingly, it is clear that $\beta$-$\ce{P_\mathrm{B}}$ is prepared by heating white phosphorus at $\pu{473 K}$ under high pressure (not black phosphorus at $\pu{473 K}$ under high pressure as stated in your textbook). I think it is a genuine mistake.
Moreover, according to literature, now more than five allotropes of phosphorous have been known:
To learn more about black phosphorus, I think Ref.3 would be helpful.
References:
- Mehdi Ghambarian, Zahra Azizi, and Mohammed Ghashghaee, “Functionalization and Doping of Black Phosphorus,” In Black Phosphorus: Synthesis, Properties and Applications; Inamuddin, Rajender Boddula, and Abdullah M. Asiri, Editors; Springer Nature Switzerland AG: Cham, Switzerland, 2020, pp. 1-30 (ISBN: 978-3-030-29555-4).
- Percy W. Bridgman, “Change of Phase under Pressure. I. The Phase Diagram of Eleven Substances with Especial Reference to The Melting Curve,” The Physical Review 1914, III(3), 153-203 (DOI: https://doi.org/10.1103/PhysRev.3.153).
- Rui Gusmão, Zdenek Sofer, and Martin Pumera, “Black Phosphorus Rediscovered: From Bulk Material to Monolayers,” Angew Chem., Int. Ed. Eng. 2017, 56(28), 8052-8072 (DOI: https://doi.org/10.1002/anie.201610512).
