substitute ac adapter

I have a cordless telephone and the AC adapter is lost. I know the details of it were as follows: Input: 230-240VAC 50Hz. Output: DC9V 350mA

I have found another adapter lying around which is labelled
Input: AC240V 50Hz. Output: DC9V 500mA

Can I use the 'found" adapter in place of the original or does it have to be 350mA the same as the original?
Thanks

i think 350mA is a minimum, 500 will be ok

of couse that filtrations of noises in the same in both adapters.

Please make sure polarity is the same.
Meaning center conductor is + or - as required.