How to add custom field to the task via CSOM?

Hello!

I'm trying to add custom fields to my programmatically created task in project 2013. Tasks are created. Then I get them and load custom fields by:

DraftProject projCheckedOut = tstProj.CheckOut();
projContext.Load(projCheckedOut.Tasks);
projContext.ExecuteQuery();

foreach (var task in projCheckedOut.Tasks)
{
	projContext.Load(task.CustomFields);
	projContext.ExecuteQuery();
}

But the each CusomFieldCollection object has only 1 field (Health, because it have a default value and created automatically). But when I load my project in Project professional i saw more than 1 field, but they are empty.

Then I tried to add a new custom field to each CusomFieldCollection of each task.

var newField = new CustomFieldCreationInformation();
newField.FieldType = CustomFieldType.TEXT;
newField.Name = "F_1";
newField.Description = "test description";
task.CustomFields.Add(newField);
task.CustomFields.Update();

New field added to the collection, but when I update the project and publish it nothing is happened.

How to add a custom field to the each task and set it value?

Or how to attach enterprise task custom field to my tasks.

I'm using Microsoft.ProjectServer.Client.