German name writing help

[boyse7en]

Any German/German speakers able to help with a formatting/spelling question?

I'm emailing a contact I made at an exhibition. Her surname as she wrote it down on my pad is "Huesemann"

I've looked her up on Linkedin, where her surname is shown as Hüsemann (with an umlaut)

Any reason why she would have spelled her name wrong/different? Is it to make typing easier for english-speakers or something?
Should I go with the "proper" spelling of her name, or use it as she provided it? I don't want to offend on first approach.