Permission issue / Access denied running windows batch file against smb share.

- Can you add or delete files, in the SMB share, from the Windows machine that is logged in with the user Jerry?
- Where is the actual batch file itself? Is it on the Windows machine or is it in the SMB share?

If adding Windows Usernames + passwords to OMV, they must be an exact match, Cap's and all.

There's a couple layers of permissions involved.
First, I wouldn't use ACL's (This is the top half of the permissions window where permissions are set by user name).

In the base shared folder, the "users" group would need read/write and make check that the associated SMB share is not configured for "Read Only".
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Try this statement in Extra Options, of the SMB share you're working with.

write list = @users

What does the batch file do? (Create, copy, paste, delete, rename, etc.)

Thinking about it, if the batch file is being executed as a scheduled task in Windows, the user account being used (for the task) might not be "Jerry". It might be "Administrator" or "System".

In Task Scheduler, look at the Task's properties. In the General Tab, under Security Options, select the user Jerry and "Run only when the user is logged on" to see if that works. If it works, you could try the option to run the task when not logged on.
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Alternately, you could try enabling the hidden Administrator account in WIndows, set a password, and add Administrator as a Linux user in OMV.

When I saw the source of your script, that was going to be the next suggestion; run it on OMV.
It's good that you're set.