The Dropdown list does not appear on the Dynamic PDF Stamp!

That won't provide the dropdown selection. The value of "str6" is the object used to set the dropdown item list. 

Use this code. 

var FormRouting = {
GetListSel:function(oLst){for(var x in oLst){if(oLst[x]>0)return x;}return null;},
initialize: function (dialog) {
// Initialize default values
var dlgInit = {
str1: "", // Job
str2: "", // Job Name
str3: "", // PM
str4: "", // Amount
str5: util.printd("mm/dd/yyyy", new Date()), // Current Date Received
str6: {"Approved":1, "Rejected":-1, "Pending Review":-1}
};

dialog.load(dlgInit);
},
commit: function (dialog) {
// Retrieve user inputs from the dialog
var oRslt = dialog.store();
this.str1 = oRslt['str1']; // Job
this.str2 = oRslt['str2']; // Job Name
this.str3 = oRslt['str3']; // PM
this.str4 = oRslt['str4']; // Amount
this.str5 = oRslt['str5']; // Date Received
this.str6 = this.GetListSel(oRslt['str6']); // Payment Type dropdown selection
console.println("Selected Payment Type: " + this.str6); // Log selected value for debugging
},
description: {
titlename: "CREDIT Approval",
align_children: "align_left",
width: 400,
height: 300,
elements: [
{
type: "cluster",
name: "CREDIT Approval",
align_children: "align_fill",
font: "dialog",
bold: true,
elements: [
{
type: "view",
align_children: "align_row",
elements: [
{ type: "static_text", name: "Job:" },
{ item_id: "str1", type: "edit_text", width: 100 },
{ type: "static_text", name: "Job Name:" },
{ item_id: "str2", type: "edit_text", width: 100 }
]
},
{
type: "view",
align_children: "align_row",
elements: [
{ type: "static_text", name: "PM:" },
{ item_id: "str3", type: "edit_text", width: 100 },
{ type: "static_text", name: "Amount:" },
{ item_id: "str4", type: "edit_text", width: 100 }
]
},
{
type: "view",
align_children: "align_row",
elements: [
{ type: "static_text", name: "Date Received:" },
{ item_id: "str5", type: "edit_text", width: 100 }
]
},
{
type: "view",
align_children: "align_row",
elements: [
{ type: "static_text", name: "Payment Type:" },
{
type: "popup",
item_id: "str6",
width: 150,
alignment: "align_fill",
items: ["Approved", "Rejected", "Pending Review"] // Dropdown options
}
]
}
]
},
{
alignment: "align_right",
type: "ok_cancel",
ok_name: "Ok",
cancel_name: "Cancel"
}
]
}
};

// Event trigger to run the dialog
if (event.source.forReal && event.source.stampName === "#Credit") {
if ('ok' == app.execDialog(FormRouting)) {
// Map the dialog values to the form fields in the document
this.getField("Job").value = FormRouting.str1; // Job
this.getField("JobName").value = FormRouting.str2; // Job Name
this.getField("PM").value = FormRouting.str3; // PM
this.getField("Amount").value = FormRouting.str4; // Amount
this.getField("DateReceived").value = FormRouting.str5; // Date Received
this.getField("PaymentType").value = FormRouting.str6; // Payment Type
}
}

Just a note about coding.  Use indents to format the code to make it more readable. Proper formatting will make it easier for you to find issues such as matching brackets. Also, don't use the identity operator ("===") unless it's really needed. For the vast majority of situations the equality operator ("==") is the correct way to go.