How to connect a SONY VPL SX226 short throw projector wirelessly to a desktop computer(does not have wifi port).

That projector is not a wireless device. Hardwired LAN (RJ-45) according to the spec sheets.

The desktop could be setup to use wireless via a wireless router but you will still need a wired LAN connection from the router to the projector.

That answer is a bit more involved and the actual details should be in the USB wireless LAN module User Manual/Guide.

It also depends on your current network configuration and settings:

In general, the following "things" need to happen and you must configure all devices accordingly.

You must assign an IP address to the wireless LAN module probably by placing it into some computer's USB drive BEFORE installing the wireless LAN module into the projector. The wireless LAN adapter may have some firmware default IP address - you will need an IP address the falls within your network's assigned IP address range. I would probably give the wireless LAN adapter a static IP address within the available range but reserved for the projector. You must also configure the wireless LAN module with respect to SSID, submask, security, wireless channel, and so forth.

If you have a network administrator he or she should be able to assist. Or at least whomever manages the router's admin functions.

I suggest that you use the desktop computer that will transmitting to the projector to do that configuration. Most likely there is a driver CD included with the wireless LAN adapter. You may also want to go online and make sure you have the most current driver with respect to the desktop's operating system.

Once the wireless LAN adapter is configured to join your network then the desktop will need to have the "projection" application necessary to identify that projector (via its IP address) in order to route the packets to the projector. The packets, of course, being the video and sound data that ends up being projected on the screen and heard on the speakers.

According to one Sony product website:

"Using a free-to-download app, it’s also easy for colleagues and students to wirelessly present their own content
stored on tablets, smartphones and other portable devices in the room."

Allows the source computer/device (the one with the images, etc. to be projected) to control the projector with respect to focus, zoom, and brightness...

So the projecting computer device gets that app installed and runs it. Most likely the app will look on the network for the destination projector but may require some indentifying element such as name or IP. Again best to use a fixed IP and note that on or very near the projector. Along with network name, submask - just to keep it all convienent.

Summary:

Desktop computer with wired ethernet connection to a wireless capable router. Necessary application software is installed to configure the UAB wireless LAN adapter so the adapter makes the projector a device on your wireless LAN.

Wireless adapter is configured and plugged into the projector.

The application on the desktop is run to find the projector and then transmit the video and audio through the network to the projector. Path is

desktop ------ethernet wire ----> Wireless router ------wireless --------> Projector.

The desktop could actually be any device running the application and could also be wireless as long as you configure it and permit it to join your network. (Generally not recommended for devices not part of your organization - security risk.) Have all presenters use the desktop and keep the AV defenses up. Probably the desktop should be dedicated for projector use and not used for anything else.

Read the manuals, plan it all out, and go step-by-step thereafter. Post any further questions, comments, error messages, accordingly.