From the picture it certainly looks like they've done this before, so that at least adds confidence.
That being said....A proper weld with a stub inside could conceivably be stronger than the original tube. The weld joining the lower and upper half doesn't appear
to be that weld; with 3/4" wall thickness, the weld should be 1 to 1.5" wide (depending on the chamfered angle) and consist of multiple passes, there also must be zero porosity and the filler metal should be appropriate for all metals used in the repair. Some type of heat treatment or stress relief or controlled cooling
might also be required to prevent brittleness or annealing.
The armature end looks pretty well made, I'm assuming that is original? Are they planning on moving it up from it's original position in the rudder? The reason I ask is that there doesn't appear to be a spacer added into the shaft to take the place of the material ground out to make the weld; do you have variability in the distance from the top of the shaft to the top of the rudder?
And finally, make sure they use epoxy
(not polyester) resin when they reglass the rudder, and high density closed cell foam when they refill it.
If you aren't sure about the weld, as suggested in other posts above you should treat this as temporary and eventually replace the shaft and armature with a solid one. The repair could last the life of the boat, it might not last 6 months.
Just thinking, I assume you're diving
the rudder to reinstall it, make absolutely sure that no water can get inside
the shaft, if that happens crevice corrosion
will destroy it in short order from within.