Welcome to the forum. You've got a good group of guys and gals here who possess a great deal of knowledge, expertise and experience (disregarding me) regarding 'ancients' and the like.
See, lots of help. One suggestion, "dear" is usually only used beginning a letter (Dear President Clinton...) or for close friends.
I couldn't find a match for the coin in acsearch. The closest I came was a contemporary 2 solidi medallion, but that weighed 8.8g. What makes you say it's fake?
It looks, based on thumb and nail size , to be about 23 or 24mm wide. I'm not an expert but the wear pattern looks odd (worn mouth/lips but intact hair) and the flatness of the fields looks weird to me (maybe I'm just not used to seeing them this worn)... I'd fall on the side of "party pooper" too.
Two things I want to say: 1. Lebanon, together with Israel, are known of making a lot of counterfeits. 2. If you paid something like a bullion-gold-price then I would not worry. But I would never buy numismatic coins in places like Lebanon/Israel. I have no opinion whether it is genuine or not.
This what makes me crazy I don't find any think like this coin I ask my self if it's fake from where they get the original one than copy it I don't find any where on net or book smaller
No no I don't found on under land I fond it with many coin like bronze coin and defiant stuff from old friend of my father he give it all to me Sorry my English not perfect
I thought he wrote that he found it in a shop in Lebanon. Anyway, I remember there was a thread where a debater asserted that he found a coin in earth, but the other debaters here questioned it. If he really found it in earth then it is genuine, and only he knows it.
Finding a coin in or on the ground does not guarantee authenticity. Fakes are sometimes salted in coin-rich areas. Perhaps forgers hope a new type will be presumed authentic due to the manner in which it was found, and the more can be produced and sold because an "authentic" example is known. Although in the OP case, as he clarified he did not find it on/in the ground.
To be clear, although I very strongly suspect it is a modern creation, I am not an expert (especially for that late Roman period) nor do I have the coin in hand for examination, so please don't take my opinion as unquestionable truth. There are no known solidi of Valens with that reverse.