1. I'll remember to see the movie with my friend.

2. I'll remember that I have to see the movie with my friend.

3. I'll remember that I will see the movie with my friend.

4. I'll remember that I can see the movie with my friend.

5. I'll remember that I must see the movie with my friend.
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What does #1 mean among the rest?

#3 is probably the closest to #1. All the others are OK, but the different verbs make slight changes in meaning.