You already pay for three tools. The month crosses them by hand. The temptation is "build an app". Sometimes the missing piece is a cable. Sometimes the cable does not exist because the process does not fit any of the three.
Integrate when
The three systems do their job. The pain is the step between them: copy a customer, an order, a status. The data already lives somewhere. Nobody rewrites it. It just does not travel.
The rule is stable. "When a quote is accepted, create the job." That is a bridge. It is not a product.
You can name the field that leaves and the field that arrives. If you cannot, you are not ready to integrate. You are ready to sit down and write the flow.
Build when
The gap is the work, not the transport. Quoting the way you quote. Planning with your rules. A close that none of the three can do. There an integration only moves a workaround from one place to another.
One of the three is real and the others are theatre. If the official number lives in a sheet "for now", do not integrate the sheet. Replace it. That is the other article: replacing the spreadsheet.
Nobody can name the system of record. Integrating three sources with no owner leaves you three truths. Pick which one wins. Then the cable.
A short test
Write one line: "When X happens in A, Y must exist in B." If that line is the month, integrate. If the month is everything that happens inside A, build A.
Do not do both "while we are at it". The bridge and the new piece are two scopes. Two quotes. Join them and you are back to an open-ended quote.
What this is not
Not a catalogue of connectors. Not a list of brands. If A and B have an official path and the rule fits in one line, use it. If the path does not exist or the rule does not fit, that is the data: change the rule or build the piece.
After
If the bridge is the work, the commission is still one job and the scope is that line. If the new piece is the work, the commission is custom software. This page only splits the cable from the tool.