If you cannot access a project line in the Timesheet or Expense table, here are the steps to check:
The project should be Active and have the status of Started or Planned (or a custom status):
The Project Status should NOT be Completed or Drafting - if a project has that status it is not available for selection.
If the status is Planned (default), it is switched to Started as soon as you book time or expenses to the project.
The Project Line Status should have the status of Started or Planned (or a custom status):
The Project Line Status should NOT be Completed - if a project line has that status it is not available for selection.
Project Line Allocation / Sharing
Allocations allow to restrict the access to the Project Line - or worded differently, that multiple people can work on that project line. If you entered a Resource on Project Line (see above), only that person has access (for selection in Timesheet and Expense). If you want to allocate additional people, click the Allocation button.
If the user who should be able to select the Project Line is on the list, make sure that the Active flag is selected.
If not, you can add the user here. If the user should just have access to this specific Project Line, select the Add user only to this line - otherwise uncheck it.
You find additional info in Project Line Allocation.