Upvote:4
Write the truth. Know that in USA immigration law material misrepresentation including by omission or fraud both lead to bars from entering the USA.
Fraud happens when an alien misrepresented a fact;to an authorized official of the United States; the fact was material;the alien did so willfully; and for the purpose of obtaining a visa, other documentation or entry into this country, or to obtain some other immigration and naturalization benefit.
https://www.uscis.gov/policymanual/Print/PolicyManual-Volume8-PartJ.html
It appears to me this clearly falls under fraud and/or willful misrepresentation IF you do not document your relationship because it is essentially inevitable that he will be asked of who is sponsoring him and the relationship to whom he is visiting. Now if perchance miraculously it is not asked in the interview, then you guys are free and clear if you don't volunteer it but I don't see how.
If the relationship is serious with potential to become something along the lines of marriage down the line, realize that a determination of fraud at this time or any time down the line will potentially make him inadmissible to the USA and barred from either getting an immigrant visa or adjusting status without getting a waiver which is difficult to get and should not be something you should even dare to knowingly fall into
Don't risk it, too much to lose and relatively little to gain.