@palindon,
No, no, a thousand times no.
That is a horrible, very non-secure way to go about it and it doesn't have to be done this way.
Make the guy a moderator (it may have a different name these days, it's the level
below administration) or administrator for your page. Try the lower level first.
This guy must use his own account to login and do his work. If he claims that he can't, he's incompetent at best and more likely a thief looking to steal your financial information.
Never,
ever hand over your passwords to anyone.
Now go change yours on Facebook and anywhere else you may use the same password, and you may want to change your security questions as well.
Yes, I am 100% serious. This is how you can end up with a stolen identity.