  A simple locally accurate uniform approximation for the nodeless wavefunction
is constructed for a {\it neutral} system of two Coulomb charges of different
masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field
for the states of positive and negative parity, ${(1s_0)}$ and ${(2p_0)}$,
respectively. It is shown that by keeping the mass and charge of one of the
bodies fixed, all systems with different second body masses are related. This
allows one to consider the second body as infinitely-massive and to take such a
system as basic. Three physical systems are considered in details: the Hydrogen
atom with (in)-finitely massive proton (deuteron, triton) and the positronium
atom $(-e,e)$. We derive the Riccati-Bloch and Generalized-Bloch equations,
which describe the domains of small and large distances, respectively. Based on
the interpolation of the small and large distance behavior of the logarithm of
the wavefunction, a compact 10-parametric function is proposed. Taken as a
variational trial function it provides accuracy of not less than 6 significant
digits (s.d.) ($\lesssim 10^{-6}$ in relative deviation) for the total energy
in the whole domain of considered magnetic fields $[0\,,\,10^4]$ a.u. and not
less than 3 s.d. for the quadrupole moment $Q_{zz}$. In order to get reference
points the Lagrange Mesh Method with 16K mesh points was used to get from 10 to
6 s.d. in energy from small to large magnetic fields. Based on the
Riccati-Bloch equation the first 100 perturbative coefficients for the energy,
in the form of rational numbers, are calculated and, using the Pad\'e-Borel
re-summation procedure, the energy is found with not less than 10 s.d. at
magnetic fields $\leq 1$\,a.u.
