I have edited the alpha channel, how to save the result?

I have a set of images. One has a background that needs to be removed. Another is a pre-made alpha channel (white on black, grayscale to be precize as it has anti-aliasing). My goal is to save the image without background as PNG with transparency.

I was able to somehow paste the second image on the alpha channel. Now the background is red (indicating alpha-channel).

Now what do I do? I tried to save as .png but got an error saying that the alpha channel can not be saved in this format.