1.js

var errorsStash = []
var errorListener = function(e) {
  errorsStash.push(e.error)
}
var unhandledRejectionListener = function(e) {
  errorsStash.push(e.reason)
}
window.addEventListener('error', errorListener)
window.addEventListener('unhandledrejection', unhandledRejectionListener)
window.__passOnToSentry__ = function() {
  delete window.__passOnToSentry__
  window.removeEventListener('error', errorListener)
  window.removeEventListener('unhandledrejection', unhandledRejectionListener)
  return errorsStash
}

2.html

<script src="https://browser.sentry-cdn.com/5.15.5/bundle.min.js" integrity="xyz" crossorigin="anonymous"></script>

3.js

Sentry.init({ dsn: 'https://xxx@yyy.ingest.sentry.io/zzz' });
var errors = window.__passOnToSentry__()
for (var i = 0; i < errors.length; i++) {
  Sentry.captureException(errors[i])
}