The present work provides a framework of Ruggiero Giuseppe Boscovich's life and teaching during the period 1763-1770. In 1763 he was called first to Pavia as a Professor of Mathematics at the local university, then to Milan (1768) as a professor in the Palatine Schools. Some unpublished manuscripts well document this important period in the life of the Jesuit and will be presented in this work. The first document, transcribed as an appendix, represents a wide list of scientific books that Boscovich suggested for the University Library of Pavia. Another important source of information is a collection of twenty-two letters, written by the Jesuit Giovanni Antonio Lecchi to Boscovich in the period 1763- 1770. This correspondence introduced even if only a little the canonical suppression of the Society of Jesus (1773).