Convert dB A to dB SPL
What you have is SPL, just weighted to match the Fletcher-Munson curves.  A weighting most closely matches the log nature of human hearing. Converting isn't exactly trivial. There are various rules of thumb around the internet, but the linearity of both of your devices will come into play. If you need any precision, the best option is to buy/borrow/steal a measurement microphone, a certified calibrator, and appropriate software, and use that as your baseline. The software will allow you to select different weightings, and see the difference between them in the frequency domain.