Catalyzes the ATP- as well as the pyrophosphate-dependent phosphorylation of a specific serine residue in HPr, a phosphocarrier protein of the phosphoenolpyruvate-dependent sugar phosphotransferase system (PTS). HprK/P also catalyzes the pyrophosphate-producing, inorganic phosphate-dependent dephosphorylation (phosphorolysis) of seryl-phosphorylated HPr (P-Ser-HPr) (By similarity). [HPr protein]-L-serine + ATP = [HPr protein]-O-phospho-L-serine + ADP + H(+) [HPr protein]-O-phospho-L-serine + H(+) + phosphate = [HPr protein]-L-serine + diphosphate This protein is composed of two complete HPrK/P domains fused in tandem. This unusual organization may lead to a separation of the two antagonistic activities in F.nucleatum, with the C-terminal copy carrying the kinase and the N-terminal copy carrying the phosphorylase. Belongs to the HPrK/P family.