POTUS writes them, and sends them out. Sometimes Liz & Natalie have statements posted which have not been put on DJT.com:
Liz Harrington & Natalie Harp post them as soon as they get them: https://mobile.twitter.com/realLizUSA/status/1489599688995184641?cxt=HHwWgoC5gczBj6wpAAAA
https://twitter.com/NatalieJHarp/status/1489608592839692291?cxt=HHwWhsCi6e7Hk6wpAAAA
And they have timestamps.