I am not sure if you can upgrade form 3.71 M33 as I have never used it but I have successfully upgraded from 3.9 to 5.00 - M33-6. On 3.9 M33 I activated WiFi and searched for updates and it states there are updates to download so it downloads the update. When you try to execute it states it needs the 500.PBP file and asks if you want it downloaded. Answer yes and it downloads it.
Once the download finishes follow the onscreen instructions and install the update. (Must have battery power at 78% or more) If you choose not to update after the downloads (or battery os too low) you can update from where you normally load your games from.
Once upgraded I copied the Update folder from the Game directory to my PC and used that to update another 3 PSP successfully by copying it to the PSP\Game Folder and executing. (All had 3.90 M33 Firmware installed
If you do a WiFi update from the PSP menu ensure that the settings for updates are pointing to the Custom Firmware and not official.
This is completed by:
1. Hold R and turn the PSP on to load the Recovery menu
2. Pusg Down Arrow to Highlight Configuration and press the X button
3. Use M33 network update (currently: Enabled)
- If it shows currently disabled press down arrow until highlight and press X button to make it enabled.
4. If Back is not Highlight press up or down until highlighted and press X
5. Press Up or Down until Exit is highlighted and press X
Obviously this only works if you are able to wirelessly connect to the network - Else you need the required files to be copied into an UPDATE folder in PSP\GAME and then execute it from the Memory Stick under the GAME Menu on the PSP.
I hope that helps