Is this a plausible reaction mechanism? (H2SO4 cyclization after Friedel-Crafts) in my undergraduate chemistry lab we synthesized the substituted benzene on the left in a Friedel-Crafts reaction. 
As a next step we're supposed to reflux for 1.5h at 90°C with concentrated sulfuric acid and obtain the product on the right. A bicyclical product. 

We have to come up with a plausible mechanism for the ring closure reaction and I am unsure that what I came up with makes sense or not. 

Thank you!



edit: this is the FC reaction we did in the first step:


The Steps for this reaction are as follows: 
To a Solution of AlCl3 in abs. DCM the following reagents were added: 
-3-chloropropionic chloride.
-p-xylene.
The reaction mixture was stirred at rt for 1h.
Then added to a mixture of 1:1 conc. HCl and ice water.
Then extracted with DCM in a separatory funnel.
Washed twice with a sat. NaCl solution. 
The organic phases were dried with MgSO4. 
The DCM was then removed in the rotary evaporator.
A yellow-orange Solution was left at the end. 
It was left to crystallize over night.

Now this is where the second part happens, the H2SO4-cyclisation reaction. 
.......
Some comments suggested that there might be a hydrolyzed intermediate with a displaced chloride. Here is my take on how that would look like:
I would propose the mechanism illustrated below, which would seem plausible in concentrated sulfuric acid: