Ever tried to recharge a non-rechargable battery?
The implausibility isn't in transmitting the energy, it's the fact that it's magically received and routed. IMO, healing lasers should at least require a "recharge" utility module that's targeted by the beam.
Ever try transferring energy from one device to another using induction? Ever try using feedback in an amplifier circuit? I can imagine firing a weapon that has matched the shield modulation so that the energy reinforces the shield harmonics rather than canceling out the shield harmonics, much like using feedback in an amplifier circuit.