Members of the public donated £10,300 for legal action against the anti-Islam activist after he posted a series of videos and Facebook posts about the incident in October.
Footage of the 15-year-old victim being pushed to the ground and having water poured on his face sparked outrage, and police continue to investigate the incident in Huddersfield.
Amid prominent media coverage, Mr Robinson posted a series of videos on his Facebook account accusing the boy of bullying and claiming “lots of Muslim gangs are beating up white English kids” in Britain.
The anti-Islam activist’s page, which was deleted last week as he was permanently banned from Facebook, had more than 1 million followers and the posts on the Huddersfield incident were viewed up to 900,000 times each.
Lawyers representing the Syrian teenager allege that the posts were defamatory, and that Facebook allowed them to spread around the world.
Solicitor Tasnime Akunjee told The Independent: “Our submission is that Mr Robinson, in tandem with Facebook, engaged in defamation of our client.”
The lawyer said the family were not demanding a specific amount of compensation, but that the case was in “unique territory” because of the teenager’s young age and the claims “being repeated numerous times across the world”.
A pre-action letter was delivered by hand to Mr Robinson’s family home on Sunday afternoon, and he has two weeks to reply.
The delivery, by YouTuber Dick Coughlan, came after the 36-year-old travelled to Finland for the launch of a film on refugees.
On a page raising money for the case Abdulnaser Youssef, of Farooq Bajwa and Co solicitors, wrote that allegations that the teenager was involved in the beating of a young English girl was false.
“We say that Tommy Robinson [whose real name is Stephen Yaxley-Lennon] ... defamed the young boy,” he added.
Lawyers hope to use part of the crowdfunded money to “penetrate the veil surrounding Stephen Yaxley-Lennon’s finances” to ensure compensation can be sought if the lawsuit succeeds.
They allege that Mr Robinson’s social media posts caused the teenager to become “the focus of countless messages of hate and threats from the extreme right wing”, and a police safety warning.
Mr Robinson’s Facebook page had a “donate” button to transfer him money at the time, but it was removed amid concern that a tool the social media giant says is for charities was abused.
Facebook deleted several of Mr Robinson’s videos for violating community standards, after the boy’s family announced their intention to sue in November.
On Tuesday, the page was removed as Mr Robinson was handed a permanent ban from Facebook and Instagram for repeatedly breaking hate speech policies.
The English Defence League founder has previously been banned from Twitter and Paypal over his activities, and his website was deleted in December.
The latest threat of legal action comes as the attorney general decides whether to launch new proceedings against Mr Robinson over alleged contempt of court that saw him jailed last year.
West Yorkshire Police said the incident at Almondbury Community School remains under investigation.
The suspect, a 16-year-old boy, has been summonsed to court for alleged assault.
The teenager had shared numerous posts from Mr Robinson’s Facebook account in the months before the incident, as well as from Britain First and other far-right accounts.