A family with members living on opposite sides of the world should be quite adept at electronic communications. If the father is willing to use email to facilitate the mortgage application, ESIGN should not be a big deal.
I assume you will convert all necessary documents and disclosures to pdf format, encrypt them, and attach them to an email message. The hardware/software/how-it-works disclosures should be fairly simple to construct. Here's everything ESIGN requires:
(B) the consumer, prior to consenting, is provided with a clear and conspicuous statement—
(i) informing the consumer of (I) any right or option of the consumer to have the record provided or made available on paper or in nonelectronic form, and (II) the right of the consumer to withdraw the consent to have the record provided or made available in an electronic form and of any conditions, consequences (which may include termination of the parties’ relationship), or fees in the event of such withdrawal;
(ii) informing the consumer of whether the consent applies (I) only to the particular transaction which
gave rise to the obligation to provide the record, or (II) to identified categories of records that may be provided or made available during the course of the parties’ relationship;
(iii) describing the procedures the consumer must use to withdraw consent as provided in clause (i) and to update information needed to contact the consumer electronically; and
(iv) informing the consumer (I) how, after the consent, the consumer may, upon request, obtain a paper
copy of an electronic record, and (II) whether any fee will be charged for such copy;
(C) the consumer—
(i) prior to consenting, is provided with a statement of the hardware and software requirements for access to and retention of the electronic records....
Pick out the disclosable items, rewrite them in your words and with your information, and put them in the same type of encrypted pdf document you will use for the loan disclosures. Add a code phrase to this sample document, such as "I want e-documents." Instruct the applicant to copy and paste or retype this phrase into an email reply and send it back to you. When you receive a proper reply, you are ESIGN-compliant and ready to send whatever disclosures you & the customer agreed.
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...gone fishing.