Here I am giving an example to transfer attachments from Opportunity to case Sobject
List insertingAttachments = new List();
List deletingAttachments = new List();
for(Attachment atch : [select id,name,body from Attachment where parentid = 'your Opportunity id' ]){
Attachment newattch = new Attachment();
newattch = atch.clone(false);
newattch.body = atch.body; // required field
newattch.name = atch.name;// required field
newattch .parentId = 'your Case id ';
insertingAttachments.add(newattch);
deletingAttachments.add(atch);
}
insert insertingAttachments;
delete deletingAttachments