Soulja Boy wants credit for being the "first" rapper to plug Icebox bling -- but the shop couldn't care less ... especially since they say there's dough he still owes.
A rep for the famed jewelry and diamond store tells TMZ ... Soulja's viral tweet from the weekend doesn't mean diddly squat to them -- in light of the (alleged) fact that there's an unresolved lawsuit they have out against the guy, which they claim he's been ducking.
Icebox sued Soulja back in 2013 for an open tab of over $60k they say he never paid -- and now tell us they haven't been able to collect ... even all these years later. At this point, Icebox says the debt has ballooned to around $200k, and of course ... they want the money they believe is long overdue.
We're told Icebox has assigned lawyers to the case in attempts to garnish the cash -- this after they say a judge ruled in their favor -- but claim SB's accounts never have more than $10k in them at a time. So, thus far, it's been a bit of a lost cause hunting it down.
In other words ... Soulja getting Twitter love for seemingly being ahead of the curve doesn't do anything for their bottom line -- despite him getting his flowers by using their name.
BTW, Icebox tells us they even dispute the notion that Soulja was the first rapper they'd worked with in Atlanta ... clarifying that while he was one of the initial big artists to get them on YouTube way back when, he was far from the first MC to cop some ice there.
Icebox's message to Soulja is quite simple ... screw the street cred -- just crank that credit card, and pay us through the phone -- or however else you want, bro.