usr/bin/find /SRC -name "*.zip" -exec usr/bin/rsync -vgoth --delete {} /DEST/ ;

$ tree
.
├── file1.zip
├── folder1
│   └── file2.zip
└── folder2
    └── subfolder
        └── file3.zip

3 directories, 3 files

$ tree $BACKUP_DESTINATION
0 directories, 0 files

$ find . -iname "*.zip" -exec rsync -vgoth {} ${BACKUP_DESTINATION} ;
[...]

$ tree $BACKUP_DESTINATION
.
├── file1.zip
├── file2.zip
└── file3.zip

0 directories, 3 files