I have no idea what you mean by "user\user" rather than just "user" It is possible to see the user specified in the form ComputerName\UserName. Is that what you meant?
Mine just shows me as UserName but if I change it to another user then it will show ComputerName\UserName at first.
There is absolutely no link with the task's Author property.
Now you have the task doing exactly what you want, you can back it up by exporting it.
- Just right-click on the task & you'll see the option to export it. It is exported as an .xml file
- It is not just a backup. It is also an opportunity to edit the task whilst in its xml form prior to re-importation. It can be edited in a text editor e.g. Notepad and displayed in a browser [the browser display can often be easier to read but you need Notepad or similar to do the editing].
- To import a task, select the folder
Event viewer tasks as before [ or another TS folder such as the
Task scheduler library folder itself that you probably use for all your other tasks] then use the
Import task … control on the right-hand side.
- To import a task with the current user identified as the account to use despite what might have been used before, before importation open the exported file [an .xml file] in, say, Notepad and delete the whole line
<UserId>...</UserId>
Delete the entire line, not just the data between those markers.
This is also what you'd often do to import the task in another computer.
- If you export some other tasks so you can see the patterns and entries used for various factors, you can also learn to alter other properties [such as battery use] in the xml before importing it.
Author is one of those. You can write any old rubbish in that line of the xml <Author>ArthurMullard</Author>
- You can change the .xml file's filename and, after re-importation, it will appear as the name of the task.
- There's no limit to what you can change in the .xml once you recognise [from examples] what needs to be in each entry.
For example, you could edit this particular task's Trigger to remove the non-useful parts of the Custom view that you started with. You could change the Subscription line
from
<Subscription><QueryList><Query Id="0" Path="System"><Select Path="System">*[System[Provider[@Name='Microsoft-Windows-Kernel-Power' or @Name='Microsoft-Windows-Power-Troubleshooter'] and (EventID=1 or EventID=42 or EventID=131 or EventID=506 or EventID=507)]]</Select></Query></QueryList></Subscription>
to
<Subscription><QueryList><Query Id="0" Path="System"><Select Path="System">*[System[Provider[@Name='Microsoft-Windows-Power-Troubleshooter'] and (EventID=1)]]</Select></Query></QueryList></Subscription>
and it would still work as intended because that Custom view provides for several other things besides the part that you are interested in.
This would work in this case but is not at all necessary. It was merely the most complex element of the task definition .xml file for me to use as an example.

So if you had not already solved your battery power problem with the task, you could have exported it, edited the .xml, deleted the original task in TS then imported the edited xml back into the
Event viewer tasks folder or another TS folder such as the
Task scheduler library folder itself that you probably use for all your other tasks.
All the best,
Denis