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We show that the Green correspondence induces an injective group homomorphism from the linear source Picard group L (B) of a block B of a finite group algebra to the linear source Picard group L (C) , where C is the Brauer correspondent of B. This homomorphism maps the trivial source Picard group T (B) to the trivial source Picard group T (C). We show further that the endopermutation source Picard group E (B) is bounded in terms of the defect groups of B and that when B has a normal defect group E (B) = L (B). Finally we prove that the rank of any invertible B -bimodule is bounded by that of B. [ABSTRACT FROM AUTHOR]