15mm solder (Yorkshire) joints will work on 15mm and 1/2 inch copper without a problem. You will need an adaptor to join 22mm and 3/4 inch though.
You can get 1/2 inch copper from compressed air component suppliers &c.
If using a yorkshire fitting to make the conversion, i always find an extra dab with solder off the roll helps to ensure a sound joint. Mebees it's me being over cautious - i dunno.
There is a whole 2.6mm difference. If you look in a plumbing outlet you can purchase a proper reducing joint which may be easier.
That's 1/2 BSP male x 15mm compression. It's used for connecting items with a 1/2 BSP female thread to pipe, not 1/2 pipe to 15mm pipe.
I've used them quite a lot in my compressed air system. Pipe sizes are metric and thread sizes imperial
PS there's an extra http:// in the link
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Hammond suddenly looks like a girl now doncha think?