  We present a theoretical study of charge transfer in collisions of excited
($n=2,3$) hydrogen atoms with He$^+$ and in collisions of excited ($n=2,3$)
helium atoms with H$^+$, extending the results of Phys. Rev. A 82 012708
(2010). A combination of quantum-mechanical and semi-classical approaches is
employed to calculate the charge-exchange cross sections at collision energies
from 0.1 eV/u up to 1 keV/u. These methods are based on accurate ab initio
potential energy curves and non-adiabatic couplings for the molecular ion
HeH$^+$. Charge transfer can occur either in singlet or in triplet states, and
the differences between the singlet and triplet spin manifolds are discussed.
The dependence of the cross section on the quantum numbers $n$ and $l$ of the
initial state is demonstrated. The isotope effect on the charge transfer cross
sections, arising at low collision energy when H is substituted by D or T, is
investigated. Finally, the impact of the present calculations on models of
laboratory plasmas is discussed.
