The company, moved by the father's poignant request, announced the good news on Nov. 24:
The family's search for the cup has gone viral.
"The chances of Ben ever using a normal cup are minimal. Maybe he never will," Carter told People. "So if, in 10 years' time, we didn't have any, it would be even harder to find some than it is today."
Ben has suffered dehydration and was taken to the hospital twice for refusing to drink five days in a row.
"Genuinely, this little blue cup controls our life," Carter told People. "We are terrified of taking it out of the house in case we lose it. It was lost at Ben's school for 24 hours once and we didn't sleep because Ben didn't drink and we were terrified — genuinely terrified."
Carter has been overwhelmed by the response, which included cup manufacturer Tommee Tippee offering a dedicated effort to find replacements.
"It's amazing that so many people have replied — really sweet," Carter said. "Everyone has been a bit down recently because of what's going on in the world, so it's just nice to know there so many kind people out there.
He is expecting 10 cups, a good start.
"I'd like to have enough cups to last me a lifetime."