Created Project Manager column field in the weekly timesheet production account.
In the weekly timesheet, record click customizes, and select the new column field.
Enter the label name as project manager
Select type as free form text
Tick time as applied to
Select display type as disabled
Source list: customer (line)
Source From: Job manager
When we select the project in the client or project tab in the weekly timesheet the corresponding PM of that project automatically appeared in the Project Manager field.