The phrase "acknowledge the willingness" is correct and usable in written English.
It can be used when recognizing or accepting someone's readiness or openness to do something.
Example: "In our meeting, we should acknowledge the willingness of the team to adapt to the new changes."
Alternatives: "recognize the readiness" or "accept the openness".
"The commission further acknowledges the willingness of Mr Jerome to make fair and appropriate concessions, both in interview and in his oral evidence.
This includes, for instance, acknowledging the parties' willingness to cooperate and try negotiations to settle the conflict, or reassuring them of the mediator's impartiality towards the issues and neutrality towards the parties.
Speaker Boehner did, however, acknowledge the president's apparent willingness to compromise on social insurance programs.
This worksheet was intended to give an overview of the person's stages of changes in relation to different recommendations of living with type 2 diabetes, and to acknowledge the option of no willingness to change.
Up till now, although the locals had expressed sympathy for my family's story and had shown a remarkable willingness to acknowledge the past crimes committed in the village and the country, there had remained a "you" and "us".
Jeremy Corbyn and other Labour MPs are right to call for the requisition of empty homes in Kensington to rehouse locally those made homeless by the fire: such action would be a test of the government's, and Kensington's, willingness to acknowledge the extent of housing inequality.
When they do discuss the commission, they justifiably laud the final report, released 50 years ago today, for its bold willingness to acknowledge the role of white racism and inequality in sparking urban unrest — and for offering a set of policy proposals designed to revitalize liberalism by forging a new "political will" to address the problems facing urban America.
The founder of the No More Page 3 campaign, Lucy Holmes, said she thought Cameron's willingness to acknowledge the dangers of online pornography while ignoring the parallel dangers of topless images on page 3 of Britain's best-read newspaper was "peculiar".
While I appreciate the Administration's willingness to acknowledge the need for more regulation of our financial markets, we cannot let a discussion about rearranging the regulatory deck chairs divert us from the fact that our housing and credit markets are in crisis, and are sinking deeper every day that we fail to take aggressive action.
