How do I claim a refund of overpaid Stamp Duty Land Tax (SDLT)?

My daughter sold her shared ownership flat in London last July. To do so she staircased to 100% by purchasing 60% (40% purchased in 2010). Contracts of sale and completion for the purchase of 60% and sale of flat were contemporaneous. My daughter unwittingly paid SDLT of £37,050.00 (should have been less anyway on account of apportionment rules) since neither she nor her solicitors were aware of the application of pre completion transaction relief (relief code 34). Her Solicitors will now claim the relief and my simple question is how should the relief be claimed? Will a letter suffice or a return resubmitted applying code 34? Will HMRC require evidence of simultaneous exchange and completion?

In order to sell 100% of her flat she had to purchase the 60% she did not own from her relevant housing association. This was achieved by finding a buyer for her flat (100%) who exchanged contracts on the same day as she exchanged for the 60%.

Completion of both transactions occurred some 2 weeks later.

My research, including, perusal of some of your material concludes that relief code 34 applies. Indeed and uncannily so the Telegraph money section highlighted an almost identical case in 2015. Their expert stated the relief should apply.