Checked my sources for Mower County Minnesota, and Adams Minnesota. Did not locate anything for Peter Theodore Phillips. There are Phillips in Mower County, but none that seem to have any connection to Peter. Did some checking on ancestry.com, you may want to check Adams County Nebraska, there is a Assumption Cemetery in Roseland Township (Peter and Marie maybe buried there) a lot of people from Luxembourg settled there.There is also the town of Adams Nebraska in Gage County. I would check with Adams County first, I think this could be helpful in your research.
Let me know if you find out anything. Will let you know if I come across anything new here.