Need Advice....

I'm currently working on an application support project in which I have very good knowledge. Now the application I'm supporting is going to another IT giant company.

I've provided kt to the resources of the company. But so far it looks those resources are finding it very hard to handle it. In few days the shadow support will get over and I'll be offboarded.

Is it wise or possible for me to get in touch with the manager's of that another company and switch to them with a good package?

If so how should I do it?