As the chat seems to have a lot of questions about SD cards on the PSP lately - I thought I'd share my experiences with both of the main types of the microSD adaptors readily available.
The first one I went for was the dual slot one - as at the time 64GB cards were reasonably priced and 128GB were expensive.
For me - I had to have 2 SD cards that were the same size for the adaptor to work, and the cards had to be formatted in the PSP itself. Once formatted it worked perfectly - however both cards are now seen as a single card and as such will not work in a PC individually. What this meant was to transfer games to the cards - I had to use the data cable and connect the PC to the PSP which was painfully slow. However the dual slot adaptor worked perfectly and apart from slow transferring of games everything was good.
Quite a while later SD card prices dropped dramatically so I bought a 200GB microSD card and a pack of single slot microSD adaptors.
The 200GB card I formatted on the PC - BUT I had to format it as Fat32 (Windows will not do this with its built in format) so I used a free program called fat32format, just make sure you read how to use the program so you don't inadvertently format the wrong drive.
This was much better for transferring file as I could put the microSD into a USB 3 card reader and have much faster transfer speeds - however the single slot adaptors are very cheaply made and if slightly out of position one of the thin plastic guides can easily snap off and rattle around inside your PSP. The way around this is to put the adaptor in just once - and anytime you want to transfer files to your device then power off the PSP and with your fingernail or a toothpick even, remove the microSD card from the adaptor while leaving the adaptor still in place in the PSP.
As with all things - now I had a good set up there was still a drawback, I had over 150 titles on the 200GB card and when going to the memory card to list the games it took ages to list all the contents - not only that but the PSP has a file limit 'per folder' (I'm not sure what the limit is - but once it reaches a certain number the PSP will not list anything after it)
The way around this is with a plugin called categories_lite, this is a great plugin that lets you create folders for each category so for example:
Now when transferring your games to your PSP you can put them in the corresponding folder - so now when you go to your memory card section there is a sub menu with your categories and when you select a category it only loads the content from that folder - so much much faster :)
This bit is a little off topic - but if you plan to use the PSP for PS1 titles then the cdda_enabler (v2 I believe) is a must have plugin (playing ridge racer with no music is just wrong lol)