How to preserve UID while saving DICOM file using SimpleITK?

I am trying to read one single DICOM file using SimpleITK and save it somewhere else. I noticed that Series Instance UID changes regardless of the fact that I am explicitly setting it.

How do I preserve the original UID?

from pathlib import Path
import SimpleITK as sitk

dicom_path = '......'
p = Path(dicom_path)

reader = sitk.ImageFileReader()
reader.SetFileName(str(p))
reader.LoadPrivateTagsOn()

image = reader.Execute()
print('Series Instance UID', image.GetMetaData('0020|000e'))
print('SOP Instance UID', image.GetMetaData('0008|0018'))
image.SetMetaData('0020|000e', image.GetMetaData('0020|000e'))

writer = sitk.ImageFileWriter()
writer.SetFileName(out_folder+case+p.name)
writer.SetUseCompression(False)
writer.Execute(image)

reader = sitk.ImageFileReader()
reader.SetFileName(out_folder+case+p.name)
reader.LoadPrivateTagsOn()

image = reader.Execute()
print('Series Instance UID', image.GetMetaData('0020|000e'))
print('SOP Instance UID', image.GetMetaData('0008|0018'))

Gives two different strings for Series UIDs. SOP UIDs stay the same though:

Series Instance UID 1.3.12.2.1107.5.1.4.74141.30000017013107011409700014483
SOP Instance UID 1.3.12.2.1107.5.1.4.74141.30000017013107011409700014570

Series Instance UID 1.2.826.0.1.3680043.2.1125.1.65790274925978549485969544082687134
SOP Instance UID 1.3.12.2.1107.5.1.4.74141.30000017013107011409700014570