Sorry about your misfortune.. See FSIMS, FAA Order 8900.1, Volume 5, Chapters 1 and 2. There is FAA guidance on lost logbooks and what is acceptable for reconstructing flight time records. The summary version is that a Notarized statement with substantiating evidence, such as rental receipts, company trip records, etc is acceptable. Also request a copy of ALL your FAA 8710 forms from AFS-760. This you can request online at FAA.GOV.