There are two foundative Equivalence Principles in General relativity:
Weak Equivalence Principle (WEP): the dynamics of a test particle in a gravitational field is independent of its mass and internal composition. (WEP is equivalent to say that the ratio between the gravitational mass $m_g$ and the inertial mass $m_i$ has a universal value $k$. This value can be considered as the scalar $1$).
Einstein equivalence principle (EEP): A frame linearly accelerated relative to an inertial frame in special relativity is LOCALLY identical to a frame at rest in a gravitational field.
Most textbooks say that "obviously" (EEP) implies (WEP) but the converse is not true.
I don't understand why the implication (EEP) $\Rightarrow$ (WEP) is true, and moreover I'd like a counterexample showing that (WEP) $\not\Rightarrow$ (EEP).