Wrapping AVI with RGBA channels in a MOV file?
You can use ffmpeg, a free command-line tool to do this.

The command is 

ffmpeg.exe -i in.avi -c:v copy out.mov


This will copy the video stream over without transcoding or dropping the alpha. The caveat here is that if MOV doesn't support the codec of the AVI video stream, then ffmpeg will fail. But, then you can simply run

ffmpeg.exe -i in.avi -c:v qtrle out.mov


This will losslessly transcode the video, keeping the alpha. The size may increase.