If the boy was on track to finish as dated in the original post, my comments won't matter any more, but I'll give them anyway.
As suggested by others, I would plan to hold the EBOR a few days before he leaves, and then work out a way to reconvene briefly to sign the papers on the correct date. If doing the EBOR early, it may take some forethought and planning. In my council, the council advancement department approves the Eagle paperwork before the EBOR is held. After they have approved it, they send it to the district Advancement Chairman so that he/she can schedule the EBOR. With some explanation, I suspect they could work out a way to get the paperwork approved at the council level and ready for the EBOR before the official qualification date.
However, if the boy is going longer on his schedule than planned, keeping him registered and working on finishing from overseas would make things very difficult. In this case, I would encourage him to get registered with an international BSA troop to finish up. What he has done here can be documented well enough that it can be finished there.
Eagle Scout 1987
OA Vigil Honor 1986
Fox - WE7-590-05-2
Currently - Troop/Team/Crew Advancement Chair & Dist Webmaster
Previously - SM, MC, CM, ACM, ADL, ASM, COR, Dist Camp Chair, PL, SPL, Scribe, Songleader, JASM, OA Chapter Officer, ...