The amplification by the sun could yield detailed images of planetary surfaces. Like a kid perusing an ant colony with a magnifying glass, the space telescope would have to slightly shift it position relative to the sun to scan the Alpha Centauri system. It might trace out a search spiral pattern that is perpendicular to its direction of motion.
An even more ambitious use of the sun's lensing abilities would be to locate a radio or optical transmitter 50 billion miles out to send a SETI message, or eavesdrop on the communications of an alien civilization. The advantage is that the transmitter would not need much power because of the sun's amplification. The disadvantage is that only one nearby star system could be targeted, at least for starters.
Transmitter/receiver probes could be mass-produced so that they are stationed all around the sun to have various sightlines to specific stars. Taking this idea a step further, two neighboring stellar civilizations might set up pairs of antennas at their respective gravitational lensing points. You might even imagine a galactic Internet where gravity lens amplified transmissions are a common strategy among chit-chatting civilizations.