  We revisit and generalize the application of a method introduced by
Latr\'emoli\`ere and Packer for constructing finitely generated projective
modules over the noncommutative solenoid C*-algebras. By realizing them as
direct limits of rotation algebras, the method constructs directed systems of
equivalence bimodules between rotation algebras that satisfy the necessary
compatibility conditions to build Morita equivalence bimodules between the
direct limit C*-algebras. In the irrational case, we use a fixed projection in
a matrix algebra over the rotation algebra satisfying a key condition to build
an equivalence bimodule at each stage following a construction of Rieffel. From
this, our main result shows that two irrational noncommutative solenoids are
Morita equivalent if and only if such a projection exists. We also make
additional observations about the Heisenberg bimodules construction studied by
the aforementioned two authors and connect the two constructions.
