"expressed their intention" is correct and usable in written English.
You can use it anytime you want to say that someone has communicated their intentions to accomplish something. For example: The speaker expressed their intention to arrive at a mutually beneficial solution.
With more countries having recently expressed their intention to take part, open government is now truly a global initiative.
Within the last year several senior and highly regarded Labour figures have expressed their intention to vote for independence.
Obama administration officials have consistently cited national security concerns and expressed their intention to keep prosecuting leakers.
When Strachey and company first expressed their intention to visit, Brenan walked the 57 miles to Almeria in two days to buy some extra furniture.
We are heartened that countries in transition, such as Myanmar and Libya, have expressed their intention to join the partnership when they are able to do so.
However, the organisers of the festival, which was sponsored by the free daily newspaper Metro, have expressed their intention to "rescue" the event on its Facebook page.
Many countries have publicly expressed their intentions to pursue the construction of new nuclear energy plants.
Policymakers have already expressed their intentions of removing restrictions on foreign ownership of state-owned and listed companies by the end of 2019, as the government looks to open its capital-hungry economy further in order to sustain its rapid growth.
Many returned migrants expressed their intentions to return north immediately, but quickly became too fearful to share their names or speak at length.
They're the only ones who can express their intention".
Candidates must apply simultaneously to both schools and express their intention to pursue the dual program.
