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I would certainly recommend a starter set of bitters, like the travel set you mentioned.  A number of bitters are available on Amazon, like this basic set of Angostura, Peychauds and Regans Orange bitters, Scrappy's classic or exotic samplers.

The little 1/4 cup Oxo angled measuring cup can stand in for a lot of jiggers.  I have several of these.

A small mesh strainer is handy for double straining even if your mixing glass or shaker set includes a Hawthorne strainer.

A citrus zester/channel knife for citrus peel garnishes is nice (I don't have that particular one so others may have more specific recommendations)

A jar of Luxardo cherries could be a nice treat to add.

Depending on your friend's existing glassware collection, a couple of rocks glass and/or smaller stemmed cocktail glasses might be a nice addition - so many contemporary "martini" glasses are bathtub sized so I often find good smaller examples at thrift stores but they are also available in shops.

Oooops! I just realized that you asked for supplies not on normal lists and everything I mentioned would be very normal - sorry!

I would certainly recommend a starter set of bitters, like the travel set you mentioned.  A number of bitters are available on Amazon, like this basic set of Angostura, Peychauds and Regans Orange bitters, Scrappy's classic or exotic samplers.

The little 1/4 cup Oxo angled measuring cup can stand in for a lot of jiggers.  I have several of these.

A small mesh strainer is handy for double straining even if your mixing glass or shaker set includes a Hawthorne strainer.

A citrus zester/channel knife for citrus peel garnishes is nice (I don't have that particular one so others may have more specific recommendations)

A jar of Luxardo cherries could be a nice treat to add.

Depending on your friend's existing glassware collection, a couple of rocks glass and/or smaller stemmed cocktail glasses might be a nice addition - so many contemporary "martini" glasses are bathtub sized so I often find good smaller examples at thrift stores but they are also available in shops.

Oooops! I just realized that you asked for supplies not on normal lists and everything I mentioned would be very normal - sorry!