When you change the web server/hosting provider, you need to request a reissue of your SSL certificate for it to work. An SSL reissue is free of charge and means that your existing certificate is replaced with a new one. A reissued SSL certificate is only valid till the actual expiration date of the original certificate.
It is recommended that for the reissue a newly generated CSR code is used.
The detailed instruction on how to reissue an SSL certificate can be found here.