I'm looking for my notebook. I remember ..... it into my suitcase when I left for work.
Q: Do I always have to fill 'gerund' in the blank?
Each English verb licenses (permits) a particular set of complement types. Remember is slightly unusual in having a different meaning with different complement types.
With gerund clauses and fused relative clauses, remember has the sense “recall, experience a memory of” a previous event:
I remember putting my noteboook into my briefcase when I left for work.
I remember where I put my notebook when I left for work—in my briefcase.
With infinitive clauses, however, it means “recall (and subsequently perform)” a future obligation:
I remembered to put my noteboook into my briefcase when I left for work.
Remember to put your noteboook into your briefcase when you leave for work.
With ‘content’ clauses it may have either meaning; the relationship between the tenses in the main clause and the subordinate clause tell you which is intended.
I remember [that] I put my notebook into my briefcase when I left for work.
I remembered [that] I must put my notebook into my briefcase when I left for work.
As this question tells us, you may encounter infinitive phrases being employed in this double sense as recently as the late nineteenth century; but this is no longer the case in Present-day English.