RHP zero with a positive phase shift
The correct way to write a transfer function featuring a single zero is \$H_1(s)=1+\frac{s}{\omega_z}\$ and a single pole is \$H_2(s)=\frac{1}{1+\frac{s}{\omega_p}}\$. The plus sign implies that when \$s\$ takes on a negative value, meaning the real zero or pole lies in the left half-plane (LHP), the corresponding \$-s_z\$ and \$-s_p\$ salient values respectively cancels \$H_1\$ and brings \$H_2\$ infinite. The phase leads for the LHP zero and lags for LHP pole.

If you now write \$H_1(s)=1-\frac{s}{\omega_z}\$ and \$H_2(s)=\frac{1}{1-\frac{s}{\omega_p}}\$, when \$s\$ takes on a positive value \$s_z\$ or \$s_p\$, meaning the real zero or pole lies in the right half-plane (RHP), the magnitudes follow the same law as for the LHP roots but the phase now lags for the zero and leads for the pole. A simple plot shows the magnitude and phase for a RHP zero and a pole.