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You would need to submit a request for military records to the national archives, where these sorts of records are deposited following a separation from the service.
There, you can submit an online request or print off a paper form to submit, using an SF-180 Form. To be able to obtain the records, you have to be next of kin. Regrettably, if you are not next of kin, then you have to have the request come from next of kin, because such records are not public information. If your mother is still living, for example, then she would need to submit the request as next of kin.
There is a archive location and I put up the military service records request page specifically.