I had the same problem with a cheapo chinese A/B. It's very, very fiddly but just a matter of balancing the thing in place while you reassemble the A/B. The large groove you see in the curved plate fits over the square peg on the end of the spring assembly. You'll need to take the needle out to do this.
There may be easier methods but the way I did it was to reassemble the spring assembly and screw it back into the body of the A/B. Pull the rear of the spring assembly back against the spring and hold it. This creates a gap so you can use a pair of tweezers to put the curved plate through the hole in the top of the body and place it over the square peg. I found it much easier to do all this before inserting the trigger. Hold the A/B tilted slightly back so the plate rests in place and refit the trigger assembly. Once the trigger is in place, you can release the spring assembly. That will allow it to move forward and the square peg will hold the plate against the trigger and stop it falling out. Finally, replace the needle and rear cover.
If you get all that done first time of trying you should light a candle to the Gods as you will have performed a miracle! I did that the first time I got everything together - then burnt myself putting the candle out as I'd put the plate in backwards
You'll have to be careful pushing the needle in. I find it helps to balance the A/B in my palm and rest the needle on my fingertips to help guide it into place.