This is the client script that needs to be uploaded to the File Cabinet. It does not need to be registered with a Script Record, but must satisfy the location of the User Event Script `clientScriptModule` (or the User Event Script's `clientScriptFileId`). More details here: http://scripteverything.com/update-record-with-button-when-viewing-in-br…

my_cs_custom_code.js

/**
 * @NApiVersion 2.x
 * @NScriptType ClientScript
 * @NModuleScope SameAccount
 */
define(['N/record', 'N/currentRecord', 'N/url'],
  /**
   * @param {record} record
   * @param {currentRecord} currentRecord
   * @param {url} url
   */
   function (record, currentRecord, url) {
      /**
       * Updates the record's fields 
       * @param {String} someText
       * @param {Number} someValue
       */
       function myClientScript(someText, someValue) {
         /** @type {CurrentRecord} */
         const cr = currentRecord.get();
         /** @type {String} */
         const cType = cr.type;
         /** @type {Number} */
         const id = cr.id;

         // Update the necessary fields...    

         record.submitFields({
            type: cType,
            id: id,
            values: {
              'custrecord_my_field1': someText,
              'custrecord_my_field2': someValue
            }
         });
    
        // Refresh the page, get URL of page then refresh...

        /** @type {String} */
        const myUrl = url.resolveRecord({
           recordType: cType,
           recordId: id,
           isEditMode: false
        });

        window.location.replace(myUrl);

     }
     
     return {myClientScript}
     
   }
}