Can a finite (by finite I mean when the projection $1$ is finite) von Neumann algebra be strongly morita equivalent to a properly infinite von Neumann algebra? 

(Strong morita equivalence is the same as Morita equivalence as a ring for $C^*$-algebras according to the theorem on page 253 of http://www.sciencedirect.com/science/article/pii/0022404982901098, see remark 1.5 for definition of strong Morita equivalence)