It may be important to consider the developmental stage of the "female body" as well. For instance, organizational vs. activational hypothesis--injecting testosterone during a critical period during development (it can be pre-natal, or during puberty) could produce permanent changes in secondary sexual characteristics and sex-specific behaviors; however, injecting testosterone after the organized system has "crystallized" (e.g. receptors are expressed in sex-specific regions, external genitalia is fully developed) may only induce temporary changes that may not be sex-specific.
As for a "female body" to develop secondary sex characteristics with testosterone injections--if these characteristics are "female" secondary sex characteristics (e.g. increased subcutaneous fat deposition in breasts in humans), it is likely that the machinery has already been organized (e.g. more "aromatase" converts testosterone to estrogen, or the location/density of androgen receptors affects sensitivity, or there is less androgen-binding protein to transport circulating testosterone), while if the secondary sex characteristics were "male" (e.g. laryngeal prominence) the testosterone injections happened during a critical development stage and/or were chronically administered (e.g. continuous administration, daily injections...).
Phoenix et al (a review cited above) did a cool experiment that might interest you.