Hi depending on how old your phone is check the following.
1.If you have Samsung messages on the old phone download Samsung messages from the Samsung store.
https://apps.samsung.com/appquery/appDetail.as?appId=com.samsung.android.messaging&cId=0000081977912. Newer Samsung devices use Google messages.
Ideally if you use same Google and Samsung accounts your messages should sync.
Follow Me, like my posts and Mark as Solution if I helped solve your Problems.