A theory of positron annihilation for exotic atoms is presented. An express
ion for the 2 gamma annihilation rate for transitions to individual residua
l atom (or ion) states recoiling at a given recoil momentum is given. Addit
ional expressions are presented for the annihilation rate integrated over r
ecoil momenta or summed over all possible final atom states. These results
are used to calculate the annihilation profiles for HPs and He(S-3(e))e(+)
and it is seen that the branching ratios to the population of the 1s ground
states are 0.9777 and 0.9996, respectively.