The phrase "acknowledge their request" is correct and usable in written English.
You can use it when responding to someone to confirm that you have received and recognized their request.
Example: "We appreciate your input and will acknowledge their request in our next meeting."
Alternatives: "confirm their request" or "recognize their request".
"OPM has recently been engaged in conversations with Congressional staff and OPM will acknowledge their requests with written communication".
The PST told BBC Sport the City Council had acknowledged their request for a £1.5m loan and were considering it.
Mr Vidler said on Thursday that Hong Kong's immigration department had acknowledged their request to continue to stay, but had not commented further.
CDERA acknowledged their requests and, based on preliminary damage assessments, initiated a Level Two response which allowed for the event to be managed at the country level with regional assistance limited to technical support and resources where required.
Mr. Cuomo, Mr. Bloomberg and the New York lawmakers, mindful that President Obama and Congressional leaders in both parties are preparing for difficult negotiations on a deficit reduction plan, acknowledged that their request would not be easily won.
The report said Poe was among those who did not fully cooperate with the Office of Congressional Ethics or did not acknowledge receipt of their request for information.
People briefed on the discussions spoke on the condition of anonymity because they are prohibited by law from discussing the content of FISA requests or even acknowledging their existence.
Their request acknowledged the inadequacy of the Cambodian justice system.
Although the protesters acknowledged it was unlikely their request would be granted, they felt the petition itself was a symbolic gesture.
Judge Rakoff denied their request, while acknowledging that the case posed broader ethical issues.
