Carol S, there is another consideration. The under barrel hammers are different on later series MX's. I think all DB81's are earlier series and that any series trigger will work, but you should call Giacomo's or other good Perazzi smith to check before buying.
Technically, the answer is "Yes." However, from gun-to-gun a trigger may not fit exactly; too tight or too loose.
Also, as mentioned above the older MX guns had a bottom barrel hammer (Right Side) that required a bottom barrel firing pin that had a machined slot on its outside where the hammer hits. Reason is that the old hammers had a small web on the outer side and when it struck the firing pin, the "gouge" in the firing pin let the hammer's web slide by it.
I have had Perazzi's here in the shop with old style hammers hitting new style bottom barrel firing pins. This is NOT A GOOD THING! With the web, when the hammer hits the rear of the firing pin, the hammer exerts sideways force on the rear on the firing pin, and after a period of time, this will cause excessive wear on the bottom firing pin hole in the receiver, eventually wearing to an elongation in the receiver giving a sloppy fit.
One can machine down the web on the old hammers to mimic the newer hammer design. I have a picture or two showing what I am trying to describe.