Your PD has broken the law by taking longer than 40 days. And there is no legitimacy to a 90 day letter they give you. That is them being silly.
According to MGL Ch. 140 Section 131, your license is good until the renewal is approved.
“(i) A license to carry or possess firearms shall be valid, unless revoked or suspended, for a period of not more than 6 years from the date of issue and shall expire on the anniversary of the licensee's date of birth occurring not less than 5 years nor more than 6 years from the date of issue; provided, however, that, if the licensee applied for renewal before the license expired, the license shall remain valid after its expiration date for all lawful purposes until the application for renewal is approved or denied.”