"enjoy" takes a nominal (a noun, a gerund). For example,
 Tom should enjoy China (while he's here).
 Tom should enjoy watching this film. I know he like's Bruce Lee.
"should" has more than one meaning. It could mean ought to or probably will or most likely will.
I suspect that difference in meaning might be the reason  and  sound 'a bit strange' to you.
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All the best.