A reasonably accurate1 rendering can be made with Celestia. Here we are at 1,500,000 km from Earth's center, on August 26, 2018 (the next full moon as I write this), at approximately the Earth-Sun L2 point.
Earth mostly but not completely eclipses the Sun's disk. The Earth and Moon appear as completely black disks in comparison to the Sun's intensity.
Because it's a full moon, the Moon is closer to us than Earth in this image. It's barely visible as a small black disk near the bottom of the image.
Going forward a few weeks to Sep 9 we get to the new moon:
The Moon looks a little smaller due to the increased distance. We also see a few sunspots.
In Celestia, a lunar eclipse from this perspective doesn't look like anything, as the Moon is just a black disk atop another black disk. I suspect this is accurate: the illumination on the Moon is very faint relative to the Sun's disk which is directly visible, and besides at the L2 point we are on the wrong side of the Moon to observe even that.
Here's first quarter, Aug 16, 2018. I've enabled artificial ambient light so the dark side of the Moon is illuminated: otherwise it wouldn't be visible in this perspective. Earth is on the right, the Moon on the left. The brightest star near the middle is Regulus, and the fuzzy spot just above it is Leo I.
Zooming in on the Moon and disabling the artificial ambient light reveals a tiny crescent, with IC 613 at the top of the frame. This is as "full" as the Moon ever gets from this perspective.
I believe the Moon should be slightly illuminated indirectly by light reflected from Earth in this view. There's some talk of planetshine being implemented in 2008 in Celestia, but apparently it was either never committed or isn't working.
1 Celestia is very accurate with regard to geometry, but has its limitations. In some of these images we see stars and possibly deep space objects, the sun's disk, and sunspots at the same time. I'm doubtful any real imaging instrument would have sufficient dynamic range to generate such an image without compositing.