can we send SMS through Pynq board using python in Pynq using some app.
I’m not sure if you know how SMS works. To send an SMS, you need to get it onto a telecoms network. The board can’t do this, but there are internet services to do this, so if your board is connected to the internet, it should be possible to do this.
This isn’t specific to PYNQ. I’d suggest you search for some of these services for something that will work for your project. As this is something you would do on the ARM processor, and not the PL, you could try search for doing this on other embedded systems e.g. RPi.