Can anyone explain how this 433MHz RF transmitter module works?
That's the simplest RF transmitter at 433.92 MHz that one can design.
That's the lowest cost RF transmitter ever.
That's an on-off RF transmitter.

T1, R1, C1, C3 and the SAW filter are the oscillator.
R2 and T2 allow the external digital command &quot;DATA&quot; to turn on and off the oscillator.
C2 is a DC blocking capacitor. You want to send AC signals only to the antenna.
L2 is an RF choke that allows the DC bias current only to arrive to the oscillator. It's a filter of AC currents.

When DATA is 3 V or 5 V then the oscillator starts oscillating and the antenna transmits RF energy in the air.
When DATA is 0 V then the oscillator stops oscillating.

SAW filter selectivity:
The selectivity of the of the oscillator is SAW filter's responsibility.
If the SAW filter is selective in frequency then the oscillator will send antenna narrow band RF signals.
If the SAW filteris selective then the RF energy sent to the antenna is well concentrated around the 433.92 MHz RF channel.
If energy is well concentrated around the 433.92 MHz RF channel, then the receiver is happy because its RF sensitivity and RF selectivity go up.

That circuit can be simulated by LT Spice free simulator.
One need to find an appropriate SAW filter at 433.92 MHz device model for LT Spice.
This in an interesting article about a spice model for a SAW device:
https://sbmicro.org.br/sforum-eventos/sforum2001/abarbosa.pdf

This in an interesting book about SAW filters:
&quot;Understanding Surface Acoustic Wave (SAW) Devices for Mobile and Wireless Applications and Design Techniques&quot;
by Colin K. Campbell

The BJT T1 must have a cut-off frequency significantly higher than 433 MHz.

NEC's BJT 2SC3357 is an NPN silicon epitaxial transistor designed for low noise amplifier at VHF, UHF and CATV band.
2SC3357 is a low-noise and high-gain bipolar transistor.
Features at bias point 1: Vce = 10 V - Ic = 7 mA - Zout = 50 Ω

NF = 1.1 dB - Ga = 8.0 dB - f = 1.0 GHz


Features at bias point 2: Vce = 10 V - Ic = 40 mA - Zout = 50 Ω

NF = 1.8 dB - Ga = 9.0 dB - f = 1.0 GHz

Ga = gain, NF = Noise figure