Trump's account was suspended for inciting violence that led to the deadly January 6 Capitol riots.
A video promoting the site is the latest post from Trump.More news: Canada halts distribution of J&J vaccine
Trump's access to social media platforms that he used as a megaphone during his presidency has been largely cut off since the Capitol riot.
The oversight board has the final say on what is removed or allowed to remain on the world's biggest social network.
"I'm hopeful the board will use this case as an opportunity to put a spotlight on Facebook's decisions about the design of its platform", Jaffer said.
Facebook Inc and Twitter Inc now have rules that give world leaders, elected officials and political candidates greater latitude than ordinary users. "It could also alter the way that social media companies treat public figures going forward".More news: NY to Ease Capacity Restrictions on Broadway Beginning May 19
The website is reportedly built by Campaign Nucleus, the digital services company created by Mr Trump's former campaign manager Brad Parscale.
But the move by Facebook and others has also drawn a torrent of criticism from Trump supporters, who argue that large tech platforms are biased and stifling opposing views.
Both Facebook and Twitter have called for input on their rules after facing intense scrutiny over their handling of USA presidential election and the storming of the Capitol by pro-Trump supporters.
The board is an independent, court-like entity for appealing content decisions on Facebook-owned platforms.More news: Canada to start to get Pfizer vaccines from the United States next week
The independent Oversight Board will announce on Wednesday whether Trump's account should be reinstated. YouTube CEO Susan Wojcicki said the suspension will be lifted when the company determines the risk of real-world violence has decreased.