I have a Nintendo and Nyko GBA/GC link.
The Nyko covers L and R but Nintendo's fits like a glove. I have had no problems with the 1st party link.
This is one of the dangers of 3rd party accessories. Nintendo designed the SP with THEIR equipment in mind, not those from companies who compete with them. You take the risk with having stuff that may be incompatible with later editions of hardware.
Worse off, your warranty is voided now since you plugged a non-liscensed product into your SP. You can get it repaired, but your warranty won't cover any of the costs.