Has any satellite proved the statement that the Sun's gravity could be used as a magnifying lens, focussing electromagnetic waves of distant galaxies or other celestial objects?
Or, is this idea, for the time being, only hypothetical?
Hubble and various others have proven this (although this was already proven from ground observatories)
There are some excellent pictures of lensed objects online, such as this galaxy arc on Hubblesite - this one was found in 2011:
That was lensed from another stellar object, but there should be no difference between the sun and other stars etc.
There kind of is a problem for doing that within the solar system.
We can imagine the sun's gravitational field to be a lens, but this is an imperfect model. The main issue with the analogy is that the deflection angle increases as you get closer. This isn't a big issue, provided that we recognize that we're talking about the creation of an Einstein ring, and not literally focusing something in the same way we would for a telescope. For the ring, the same relationship between angle of deflection and focal length holds.
All spherically symmetric bodies have the same gravitational field around them. This is true in both classical mechanics and general relativity, and the idea holds right up until you get to the surface of the body. Now here's the problem:
If you calculate it, the radius that gets you the right angle of deflection to form an Einstein ring (of a far-away object) with the sun will be below the radius of the sun. This obviously isn't useful because the light will not pass through the interior (defined by the photosphere) of the sun. To walk through the logic a little bit more, imagine these steps:
For the minimal requirements to do such a mission, we will start out requiring that the radius at which the deflection takes place will be greater than the sun's radius itself. That will give a relatively low angle of deflection. That will then give a long focal length - certainly more than 1 AU, which is kind of the assumption implicit in the question.
Could Voyager possibly see an Einstein ring produced of a distant star when looking at the sun? I haven't done the calculation, but yes, that would be possible if the math checks out. So my is that yes you can do this, but only at a huge distance, certainly not from the inner solar system where we reside.