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how to add moment.js in my code? Is it still possible to work with this library? Is it recommended?

I'm using it. Just have to add it in the define, like:

define([
  'N/query',
  'N/record',
  'N/runtime',
  './search/search.js',
  'N/url',
  'SuiteScripts/ZuriSDF/libs/moment.js'
], function (
  query,
  record,
  runtime,
  search,
  url,
  moment
)

if you are still trying to set the duedate, then your problem is still using Dates

trying to use moment to manipulate a Date will not fix your problems

The official momentjs documentation suggests only using it for legacy projects and moving to a newer library for new development. There are several suggestions on the momentjs website. 

unfortunately the javascript environment in suitescript is old enough to be considered legacy

notably the newer date based libraries use Internationalization apis, which suitescript does not implement