Unfortunately, Android does not provide us with a means to record directly from another application. We can only record from the hardware mic. But if you run Hi-Q MP3 Voice Recorder in the background, you can still record Skype conversation, but the quality might not be optimal.

If you are unsure with the recordings’ quality through your phone, please try Hi-Q MP3 Voice Recorder free version before purchasing: Hi-Q MP3 Voice Recorder (Free)

Starting from Android KitKat (4.4),  downloaded apps are only allowed to write to a certain part of a removable SD card.

When you change the location of stored recordings from the app Settings, choose “App folder on SD Card”. 

Then when you want to access the recordings on the SD Card directly from your PC, the folder is located in: Android > data > com.hiqrecorder.full > files > Recordings. Alternatively, use the Wi-Fi Transfer feature to move the files to your PC.