Unfortunately, there is no easy way to save a project to an earlier version. You have to build the model from scratch, sorry.
Are you using Explicit Dynamics? That calculates a time step that can be tiny and result in long solution times. For example, if the solver estimates that it will take 300 hours on your laptop because the time step is 1e-7 seconds, that same time step will be present on the lab computer. What is the clock speed of your laptop? You will find the lab computer clock speed is not going to be much faster than your laptop (it may even be slower), it is certainly unlikely to be twice as fast and even if it was, that is still 150 hours of solution time, which is intolerable.
What you need to do is make changes to the model to increase the time step from 1e-7 to 1e-6. then the model will take only 30 hours on the laptop computer.
Here are some changes you can make to your Explicit Dynamics model to make it solve in less time. You can edit the density of the material to artificially reduce the time it takes to solve. For example, if you multiply the density by a factor of 25, the solution will take 1/5 of the time to compute the solution.
Another change is to increase the minimum element size. Look at the Mesh Metric called Characteristic Length. If you can increase the minimum length by a factor of 4, the solution will compute in 1/4 of the time.
If you do both those things, the solution will take 1/20 of the time to compute. Now that 300 hours becomes 15 hours on the laptop, which is tolerable.
None of the above applies to Transient Structural models, which use a completely different solver.