In 2001 I watched a great documentary about Shakespeare. And this was the reason that novel books attracted my attention. I was also learning English at the moment.
Is it possible to use "at the moment" in the story instead of "at that moment", or incorrect?
I probably found a good answer, quoted below, to my question but I am not sure as to its credibility.
"I wasn't feeling like it at the moment." is perfectly good English. The same as, "He wasn't working at the time." However, most native speakers would say, "At the moment, I wasn't in the mood to watch a movie." You don't need the demonstrative there either, although you can put it in if you like.
"at the moment" isn't like "now" that has to be replaced by "then" in the past. It works fine in any present or past tense.
A quote about using "at the moment" in the past tense from COCA corpus
Over the next several months I recorded many of Ricardo's chants until my tape recorder was destroyed, fused by a lightning strike. As this occurred immediately after Ricardo had summoned me to his presence and I had replied that I was busy at the moment, the event did not lessen his considerable pride or reduce his reputation as the most powerful shaman of the area.
A quote from Google books
I texted him back to tell him I was busy at the moment and that I would contact him the next day. He said okay and that was that. As usual I put that out of my mind so that I could give my date my full attention.
By WENDY RICHARDS - 2013
You can search for more in Google books using I was busy at the moment here.