'immediately submit' is a perfectly acceptable and usable phrase in written English.
You can use it when you want to emphasize that something must be submitted quickly or soon. Example: All team members must immediately submit their reports by Friday.
"We would immediately submit a proposal," said the company's president, Jon Mapel.
More trade means that President Obama should immediately submit, and Congress should immediately ratify, the pending free-trade agreements.
Senior opposition figure Lim Kit Siang said Najib must immediately submit to justice to avoid further harming Malaysia's image.
They also abandoned their insistence that Yonkers immediately submit a three-year balanced budget plan, saying they now expect it no later than 15 days after the Legislature completes the overdue state budget.
But on Monday the Supreme Court ruled that Ross would not have to immediately submit to a deposition about his role in the question's inclusion, though the deposition of Gore and other evidence-gathering was allowed to proceed.
After returning from their conference, recipients are required to immediately submit a short (half page to one page) report of all activities undertaken with support from the YSPH Conference Travel Fund.
And upon that, it was immediately submitted for tests.
She immediately submitted a request to the Metropolitan Police for a copy.
The novel was finished in 1945 and immediately submitted to a number of publishers.
Demjanjuk's lawyer, Ulrich Busch, immediately submitted an appeal to the judge to abandon the trial on the grounds that his client had "been a victim".
I somehow regained my seated position on the board and immediately submitted again to gravity, zooming down, down, down, until I slid to a gentle stop amid applause from fellow boarders.
