  Recent trend of research indicates that not only massive but also massless
(asymptotic Newtonian mass zero) wormholes can reproduce post-merger initial
ring-down gravitational waves characteristic of black hole horizon. In the
massless case, it is the non-zero charge of other fields, equivalent to what we
call here the "Wheelerian mass", that is responsible for mimicking ring-down
quasi-normal modes. In this paper, we enquire whether the same Wheelerian mass
can reproduce black hole observables also in an altogether different
experiment, viz., the strong field lensing. We examine two classes of massless
wormholes, one in the Einstein-Maxwell-Dilaton (EMD) theory and the other in
the Einstein-Minimally-coupled-Scalar field (EMS) theory. The observables such
as the radius of the shadow, image separation and magnification of the
corresponding Wheelerian masses are compared with those of a black hole
(idealized SgrA* chosen for illustration) assuming that the three types of
lenses share the same minimum impact parameter and distance from the observer.
It turns out that, while the massless EMS\ wormholes can closely mimic the
black hole in terms of strong field lensing observables, the EMD wormholes show
considerable differences due to the presence of dilatonic charge. The
conclusion is that masslessless alone is enough to closely mimic Schwarzschild
black hole strong lensing observables in the EMS theory but not in the other,
where extra parameters also influence those observables. The motion of timelike
particles is briefly discussed for completeness.
