There is no such thing as adjusting abroad.
An I-601 can only be filed after the beneficiary has been found inadmissible. Since he would now be seeking an immigrant visa, he would need to be denied at the embassy before the I-601 could be filed.
As already stated, leaving without AP automatically voided his pending I-485.
Since your case is messy I would suggest consulting with an experienced immigration attorney.
How I suspect you need to proceed would be needing to file an I-824 to request the approved I-130 be forwarded to the NVC. You then go through that process until he had his interview abroad and was denied. At that point the I-601 could be filed, and if successful he could finally receive his immigrant visa following a second interview.
Realistically you're looking at ~1-2 years from now for this to play out.
This is a cautionary tale in why you should always obtain AP when adjusting status even if you have no concrete plans to travel. In this specific situation it's possible he may have had issues trying to re-enter even with AP, depending on what the exact nature of his original "fraudulent entry" was.
OP is original poster, you. I can only repeat that leaving without AP while an I-485 is pending means automatic denial and there is no way to "resurrect" the I-485. "Adjusting abroad" does NOT exist. Whoever told you it did was simply wrong.
Your husband needs his immigrant visa denied before he can file the I-601. Hopefully you have a copy of the package so you can re-submit it.
