AMPScript - Insert subscriber into list (including Publication List) - Details: https://vijayasankarn.wordpress.com/2021/02/24/marketing-cloud-insert-into-subscriber-list-using-ampscript/

AddToSubscriberList.amp

%%[
    /* Replace with your list ID */
    SET @ListID = "<YOUR_ID>"
    SET @SubscriberKey = "<Subscriber_Key>"
 
    SET @rr = CreateObject("RetrieveRequest")
    SetObjectProperty(@rr,"ObjectType","ListSubscriber")
    AddObjectArrayItem(@rr,"Properties","SubscriberKey")
    AddObjectArrayItem(@rr,"Properties","ListID")
    
    SET @sfpl = CreateObject("SimpleFilterPart")
    SetObjectProperty(@sfpl,"Property","ListID")
    SetObjectProperty(@sfpl,"SimpleOperator","equals")
    AddObjectArrayItem(@sfpl,"Value",@ListID)
 
    SET @sfpr = CreateObject("SimpleFilterPart")
    SetObjectProperty(@sfpr,"Property","SubscriberKey")
    SetObjectProperty(@sfpr,"SimpleOperator","equals")
    AddObjectArrayItem(@sfpr,"Value",@SubscriberKey)
 
    SET @cf = CreateObject("ComplexFilterPart")
    SetObjectProperty(@cf,"LeftOperand",@sfpl)
    SetObjectProperty(@cf,"RightOperand",@sfpr)
    SetObjectProperty(@cf,"LogicalOperator","AND")
 
    SetObjectProperty(@rr,"Filter",@cf)
    
    SET @listFields = InvokeRetrieve(@rr)
 
    /* Update only when it is not already present */
    IF NOT(RowCount(@listFields)) THEN
        SET @sub = CreateObject("Subscriber")
        SetObjectProperty(@sub,"SubscriberKey",@SubscriberKey)

        set @lSub = CreateObject("SubscriberList")
        SetObjectProperty(@lSub,"ID",@ListID)
        SetObjectProperty(@lSub,"Status","Active")
        AddObjectArrayItem(@sub,"Lists",@lSub)

        SET @updateStatus = InvokeUpdate(@sub)

        IF @updateStatus == "OK" THEN
          Output(v("Subscriber added to the list successfully!"))
        ELSE
          Output(v("There was a problem adding the subscriber added to the list!"))
        ENDIF
    ELSE
        Output(v("Subscriber already exists in list"))
    ENDIF
]%%