Legality of Digital Permit Book for FMCSA Compliance

390.32b Electronic Documents and Signatures. ( USA and Canada )

Electronic records or documents. Any person or entity required to generate, maintain, or exchange documents to satisfy requirements in chapter III of subtitle B of title 49, Code of Federal Regulations (49CFR300–399) may use electronic methods to satisfy those requirements.
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Read more here in Part b.

IRP Plan 600b Credentials for Apportioned Registration. ( USA and Canada)
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A Base Jurisdiction shall require that the Cab Card be carried in the Vehicle for which it is issued. A Base Jurisdiction may issue a Cab Card in paper or as an electronic image. Jurisdictions must accept paper originals, legible paper copies, or legible electronic images, whichever is presented by the Registrant and regardless of the method by which the Cab Card was issued by the Base Jurisdiction.
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Read more here on Page 40.

IFTA R620 Articles of Agreement & Possession of License. ( USA and Canada)
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Each licensee shall be issued one IFTA license or cab card in paper or as an electronic image. The licensee is required to make legible paper copies or electronic images of the license so that one and a copy shall be carried in each vehicle. Member jurisdictions must accept paper originals, paper copies, or electronic images of IFTA licenses, whichever is presented by the licensee and regardless of the method by which the license was initially issued by the base jurisdiction. A vehicle will not be considered to be operating under this Agreement unless there is a copy of the license in the vehicle, or an electronic image is made available at the time it is requested.

Read more here on Page 28.