As a preliminary step, you should bear in mind that most countries enforce controls on importing / exporting plant material. This is so that pests and diseases and invasive plants do not get spread around the globe and to protect endangered plant species. Before you consider which propagation method to use, you should make sure about the legalities first! It is often easier to import / export seed than plant material such as cuttings.
Having said all of that, I'm not sure which direction your friend is taking the plant material in. Hydrangeas are native to southern and eastern asia, so perhaps she hopes to bring some here? Although you do talk about posting one to her. In the UK it is most common to propagate hydrangeas from cuttings. Softwood should be taken from late spring to midsummer, semi-ripe in midsummer and hardwood in winter. Seeds should be sown in spring.
Hydrangeas are wonderful plants so I hope that you will both be able to enjoy them.
I hope it all goes well.